ScholarBank@NUShttps://scholarbank.nus.edu.sgThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Thu, 09 Dec 2021 14:36:30 GMT2021-12-09T14:36:30Z50711- High performance quadratic classifier and the application on PenDigits recognitionhttps://scholarbank.nus.edu.sg/handle/10635/44241Title: High performance quadratic classifier and the application on PenDigits recognition
Authors: Zhao, Z.J.; Sun, J.; Ge, S.S.
Abstract: A nonconvex quadratic classifier is proposed for pattern recognition. The classifier is obtained by solving a second-order cone optimization problem on the training data set. Numerical results are presented to compare this classifier with the Gaussian classifier and k-NN classifiers. Regarding to the application of hand written digits recognition, the computational result shows that the proposed quadratic classifier always achieves highest correctness in the testing stage although it takes the longest computational time in the training stage. © 2007 IEEE.
Mon, 01 Jan 2007 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/442412007-01-01T00:00:00Z
- Semismooth homeomorphisms and strong stability of semidefinite and Lorentz complementarity problemshttps://scholarbank.nus.edu.sg/handle/10635/44218Title: Semismooth homeomorphisms and strong stability of semidefinite and Lorentz complementarity problems
Authors: Pang, J.-S.; Sun, D.; Sun, J.
Abstract: Based on an inverse function theorem for a system of semismooth equations, this paper establishes several necessary and sufficient conditions for an isolated solution of a complementarity problem defined on the cone of symmetric positive semidefinite matrices to be strongly regular/stable. We show further that for a parametric complementarity problem of this kind, if a solution corresponding to a base parameter is strongly stable, then a semismooth implicit solution function exists whose directional derivatives can be computed by solving certain affine problems on the critical cone at the base solution. Similar results are also derived for a complementarity problem defined on the Lorentz cone. The analysis relies on some new properties of the directional derivatives of the projector onto the semidefinite cone and the Lorentz cone.
Wed, 01 Jan 2003 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/442182003-01-01T00:00:00Z
- An analytic center cutting plane method for semidefinite feasibility problemshttps://scholarbank.nus.edu.sg/handle/10635/44210Title: An analytic center cutting plane method for semidefinite feasibility problems
Authors: Sun, J.; Toh, K.-C.; Zhao, G.
Abstract: Semidefinite feasibility problems arise in many areas of operations research. The abstract form of these problems can be described as finding a point in a nonempty bounded convex body Γ in the cone of symmetric positive semidefinite matrices. Assume that Γ is defined by an oracle, which for any given m × m symmetric positive semidefinite matrix Ŷ either confirms that Ŷ ε Γ or returns a cut, i.e., a symmetric matrix A such that Γ is in the half-space {Y : A · Y ≤ A · Ŷ}. We study an analytic center cutting plane algorithm for this problem. At each iteration, the algorithm computes an approximate analytic center of a working set defined by the cutting plane system generated in the previous iterations. If this approximate analytic center is a solution, then the algorithm terminates; otherwise the new cutting plane returned by the oracle is added into the system. As the number of iterations increases, the working set shrinks and the algorithm eventually finds a solution to the problem. All iterates generated by the algorithm are positive definite matrices. The algorithm has a worst-case complexity of O* (m3/ε2) on the total number of cuts to be used, where ε is the maximum radius of a ball contained by Γ.
Tue, 01 Jan 2002 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/442102002-01-01T00:00:00Z
- Semismooth matrix-valued functionshttps://scholarbank.nus.edu.sg/handle/10635/44209Title: Semismooth matrix-valued functions
Authors: Sun, D.; Sun, J.
Abstract: Matrix-valued functions play an important role in the development of algorithms for semidefinite programming problems. This paper studies generalized differential properties of such functions related to nonsmooth-smoothing Newton methods. The first part of this paper discusses basic properties such as the generalized derivative, Rademacher's theorem, B-derivative, directional derivative, and semismoothness. The second part shows that the matrix absolute-value function, the matrix semidefinite-projection function, and the matrix projective residual function are strongly semismooth.
Tue, 01 Jan 2002 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/442092002-01-01T00:00:00Z
- A Distributionally Robust Approach for a Class of Three-Stage Stochastic Linear Programshttps://scholarbank.nus.edu.sg/handle/10635/191940Title: A Distributionally Robust Approach for a Class of Three-Stage Stochastic Linear Programs
Authors: Sun, Jie; Li, Bin; Teo, Kok Lay; Yu, Changjun; Zhang, Min
Tue, 01 Jan 2019 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1919402019-01-01T00:00:00Z
- A new constraint qualification and a second-order necessary optimality condition for mathematical programming problemshttps://scholarbank.nus.edu.sg/handle/10635/44059Title: A new constraint qualification and a second-order necessary optimality condition for mathematical programming problems
Authors: He, Y.; Sun, J.
Abstract: We present a new condition of constraint qualification that involves a second-order tangent set. Based on this constraint qualification, we establish a second-order necessary optimality condition for mathematical programming problems. The new qualification condition is weaker than the popular constraint qualification of Robinson. An example is presented to show the usefulness of the result. The results can be applied to problems with abstract feasible sets as well as to problems with feasible regions defined explicitly by nonconvex equalities and inequalities. © Yokohama Publishers.
Sat, 01 Jan 2011 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/440592011-01-01T00:00:00Z
- Second-order cone reformulation and the price of anarchy of a robust nash-cournot gamehttps://scholarbank.nus.edu.sg/handle/10635/43963Title: Second-order cone reformulation and the price of anarchy of a robust nash-cournot game
Authors: Han, D.; Lo, H.K.; Sun, J.; Yang, H.
Abstract: We study an n-person Nash-Cournot game with incomplete information, in which the opponents' strategies are only known in a perturbed set and the players try to minimize their worst-case costs, which can vary due to data uncertainty. We show that in several interesting cases, this game can be reformulated as second-order cone optimization problems. We also derive a bound of the price of anarchy for this game, which is a bound on the ratio between the cost at the robust Nash-Cournot equilibria and the cost at the system optima. © 2010 Yokohama Publishers.
Fri, 01 Jan 2010 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/439632010-01-01T00:00:00Z
- Third-party warehousing contract with commitments and adjustment optionshttps://scholarbank.nus.edu.sg/handle/10635/140258Title: Third-party warehousing contract with commitments and adjustment options
Authors: Chen, Frank Y.; Hum, Sin Hoon; Sun, Jie
Tue, 01 Dec 1998 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1402581998-12-01T00:00:00Z
- An analytic center based column generation algorithm for convex quadratic feasibility problemshttps://scholarbank.nus.edu.sg/handle/10635/45026Title: An analytic center based column generation algorithm for convex quadratic feasibility problems
Authors: Luo, Z.-Q.; Sun, J.
Abstract: We consider the analytic center based column generation algorithm for the problem of finding a feasible point in a set defined by a finite number of convex quadratic inequalities. At each iteration the algorithm computes an approximate analytic center of the set defined by the intersection of quadratic inequalities generated in the previous iterations. If this approximate analytic center is a solution, then the algorithm terminates; otherwise a quadratic inequality violated at the current center is selected and a new quadratic cut (defined by a convex quadratic inequality) is placed near the approximate center. As the number of cuts increases, the set defined by their intersection shrinks and the algorithm eventually finds a solution to the problem. Previously, similar analytic center based column generation algorithms were studied first for the linear feasibility problem and later for the general convex feasibility problem. Our method differs from these early methods in that we use "quadratic cuts" in the computation instead of linear cuts. Moreover, our method has a polynomial worst case complexity of O(n ln 1/ε) on the total number of cuts to be used, where n is the number of convex quadratic polynomial inequalities in the problem and ε is the radius of the largest ball contained in the feasible set. In contrast, the early column generation methods using linear cuts can only solve the convex quadratic feasibility problem in pseudopolynomial time.
Thu, 01 Jan 1998 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/450261998-01-01T00:00:00Z
- A simplex method and its implementation for network piecewise linear programminghttps://scholarbank.nus.edu.sg/handle/10635/45027Title: A simplex method and its implementation for network piecewise linear programming
Authors: Sun, J.; Tsai, K.H.
Abstract: Network piecewise linear programming is a useful model in operations research. It could be solved as network linear programming through a reformulation approach which greatly increases the number of variables. This paper describes a direct simplex algorithm and its implementation for network piecewise linear programming. By allowing nonbasic variables to take breakpoint values and using nominal costs at breakpoints of the objective function, this method keeps the number of variables in the original level and simplifies the computation of the reduced cost. This is important for applications in which the number of breakpoints is large; for instance, the stochastic network flow problem and the piecewise linearized convex network program. The method takes good advantage of tree data structures and combines ratio test with the computation of reduced costs. Computational experiment is conduced on the 40 benchmark network programs of Klingman et al. by replacing the linear costs with piecewise linear costs. The result of the test shows that solving a network problem with piecewise linear cost is not much harder than solving a linear problem on the same network.
Wed, 01 Jan 1997 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/450271997-01-01T00:00:00Z
- On piecewise quadratic Newton and trust region problemshttps://scholarbank.nus.edu.sg/handle/10635/45028Title: On piecewise quadratic Newton and trust region problems
Authors: Sun, J.
Abstract: Some recent algorithms for nonsmooth optimization require solutions to certain piecewise quadratic programming subproblems. Two types of subproblems are considered in this paper. The first type seeks the minimization of a continuously differentiable and strictly convex piecewise quadratic function subject to linear equality constraints. We prove that a nonsmooth version of Newton's method is globally and finitely convergent in this case. The second type involves the minimization of a possibly nonconvex and nondifferentiable piecewise quadratic function over a Euclidean ball. Characterizations of the global minimizer are studied under various conditions. The results extend a classical result on the trust region problem.
Wed, 01 Jan 1997 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/450281997-01-01T00:00:00Z
- Applying a Newton method to strictly convex separable network quadratic programshttps://scholarbank.nus.edu.sg/handle/10635/44991Title: Applying a Newton method to strictly convex separable network quadratic programs
Authors: Sun, J.; Kuo, H.
Abstract: By introducing quadratic penalty terms, a strictly convex separable network quadratic program can be reduced to an unconstrained optimization problem whose objective is a continuously differentiable piecewise quadratic function. A recently developed nonsmooth version of Newton's method is applied to the reduced problem. The generalized Newton direction is computed by an iterative procedure which exploits the special network data structures that originated from the network simplex method. New features of the algorithm include the use of min-max bases and a dynamic strategy in computation of the Newton directions. Some preliminary computational results are presented. The results suggest the use of "warm start" instead of "cold start.".
Thu, 01 Jan 1998 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/449911998-01-01T00:00:00Z
- Computing the optimal replenishment policy for inventory systems with random discount opportunitieshttps://scholarbank.nus.edu.sg/handle/10635/42986Title: Computing the optimal replenishment policy for inventory systems with random discount opportunities
Authors: Feng, Y.; Sun, J.
Abstract: The paper considers the optimal control of a single-item continuous-review inventory system with random demand and discount opportunities. Items can always be purchased with the regular order setup and variable costs. However, when a discount opportunity occurs, they can also be purchased with a different setup cost and a lower variable cost. Demands for individual items and discount opportunities occur according to independent Poisson processes. The paper proposes an algorithm to compute the parameters of the optimal replenishment policy, which has been shown to be an (r, R, d, D) policy where r < R, r ≤ d, and d < D. Under an (r, R, d, D) policy, when the inventory position drops to the level r, an order is placed with the regular costs to increase the inventory position to R; and when a discount opportunity occurs at or below d, an order is placed with the discount costs to increase the inventory position to D. The algorithm is based on a bisection search procedure to minimize the long-run average cost and is finitely convergent.
Mon, 01 Jan 2001 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/429862001-01-01T00:00:00Z
- A predictor-corrector algorithm for a class of nonlinear saddle point problemshttps://scholarbank.nus.edu.sg/handle/10635/45067Title: A predictor-corrector algorithm for a class of nonlinear saddle point problems
Authors: Sun, J.; Zhu, J.; Zhao, G.
Abstract: An interior path-following algorithm is proposed for solving the nonlinear saddle point problem minimax cT x + φ(x) + bT y - ψ(y) -yT Ax subject to (x, y) ∈ X x Y ⊂ Rn x Rm, where φ(x) and ψ(y) are smooth convex functions and X and Y are boxes (hyperrectangles). This problem is closely related to the models in stochastic programming and optimal control studied by Rockafellar and Wets (Math. Programming Studies, 28 (1986), pp. 63-93; SIAM J. Control Optim., 28 (1990), pp. 810-822). Existence and error-bound results on a central path are derived. Starting from an initial solution near the central path with duality gap O(μ), the algorithm finds an ∈-optimal solution of the problem in O(√m + n| log μ/∈|) iterations if both φ(x) and ψ(y) satisfy a scaled Lipschitz condition.
Wed, 01 Jan 1997 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/450671997-01-01T00:00:00Z
- On the rate of local convergence of high-order-infeasible-path-following algorithms for P*-linear complementarity problemshttps://scholarbank.nus.edu.sg/handle/10635/45068Title: On the rate of local convergence of high-order-infeasible-path-following algorithms for P*-linear complementarity problems
Authors: Zhao, G.; Sun, J.
Abstract: A simple and unified analysis is provided on the rate of local convergence for a class of high-order-infeasible-path-following algorithms for the P*-linear complementarity problem (P*-LCP). It is shown that the rate of local convergence of a ν-order algorithm with a centering step is ν+1 if there is a strictly complementary solution and (ν+1)/2 otherwise. For the ν-order algorithm without the centering step the corresponding rates are ν and ν/2, respectively. The algorithm without a centering step does not follow the fixed traditional central path. Instead, at each iteration, it follows a new analytic path connecting the current iterate with an optimal solution to generate the next iterate. An advantage of this algorithm is that it does not restrict iterates in a sequence of contracting neighborhoods of the central path.
Fri, 01 Jan 1999 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/450681999-01-01T00:00:00Z
- Global linear and local quadratic convergence of a long-step adaptive-mode interior point method for some monotone variational inequality problemshttps://scholarbank.nus.edu.sg/handle/10635/45072Title: Global linear and local quadratic convergence of a long-step adaptive-mode interior point method for some monotone variational inequality problems
Authors: Sun, J.; Zhao, G.
Abstract: An interior point (IP) method is proposed to solve variational inequality problems for monotone functions and polyhedral sets. The method has the following advantages: 1. Given an initial interior feasible solution with duality gap μ0, the algorithm requires at most O[n log(μ0/ε)] iterations to obtain an ε-optimal solution. 2. The rate of convergence of the duality gap is q-quadratic. 3. At each iteration, a long-step improvement is allowed. 4. The algorithm can automatically transfer from a linear mode to a quadratic mode to accelerate the local convergence.
Thu, 01 Jan 1998 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/450721998-01-01T00:00:00Z
- A quadratically convergent polynomial long-step algorithm for a class of nonlinear monotone complementarity problemshttps://scholarbank.nus.edu.sg/handle/10635/45083Title: A quadratically convergent polynomial long-step algorithm for a class of nonlinear monotone complementarity problems
Authors: Sun, J.; Zhao, G.
Abstract: Several interior point algorithms have been proposed for solving nonlinear monotone complementarity problems. Some of them have polynomial worst-case complexity but have to confine to short steps, whereas some of the others can take long steps but no polynomial complexity is proven. This paper presents an algorithm which is both long-step and polynomial. In addition, the sequence generated by the algorithm, as well as the corresponding complementarity gap, converges quadratically. The proof of the polynomial complexity requires that the monotone mapping satisfies a scaled Lipschitz condition, while the quadratic rate of convergence is derived under the assumptions that the problem has a strictly complementary solution and that the Jacobian of the mapping satisfies certain regularity conditions. © 2000 OPA (Overseas Publishers Association) N.V. Published by license under the Gordon and Breach Science Publishers imprint.
Sat, 01 Jan 2000 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/450832000-01-01T00:00:00Z
- Quadratic convergence of a long-step interior-point method for nonlinear monotone variational inequality problemshttps://scholarbank.nus.edu.sg/handle/10635/45085Title: Quadratic convergence of a long-step interior-point method for nonlinear monotone variational inequality problems
Authors: Sun, J.; Zhao, G.Y.
Abstract: This paper offers an analysis on a standard long-step primaldual interior-point method for nonlinear monotone variational inequality problems. The method has polynomial-time complexity and its q-order of convergence is two. The results are proved under mild assumptions. In particular, new conditions on the invariance of the rank and range space of certain matrices are employed, rather than restrictive assumptions like nondegeneracy.
Thu, 01 Jan 1998 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/450851998-01-01T00:00:00Z
- Analysis of optimal boundary control for a three-dimensional reaction-diffusion systemhttps://scholarbank.nus.edu.sg/handle/10635/174613Title: Analysis of optimal boundary control for a three-dimensional reaction-diffusion system
Authors: Yang W.; Sun J.; Zhang S.
Abstract: This paper is concerned with optimal boundary control of a three dimensional reaction-diffusion system in a more general form than what has been presented in the literature. The state equations are analyzed and the optimal control problem is investigated. Necessary and sufficient optimality conditions are derived. The model is widely applicable due to its generality. Some examples in applications are discussed. © 2017 Federacion Argentina de Cardiologia. All right reserved.
Sun, 01 Jan 2017 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1746132017-01-01T00:00:00Z
- A primal-dual interior-point method capable of rapidly detecting infeasibility for nonlinear programshttps://scholarbank.nus.edu.sg/handle/10635/196192Title: A primal-dual interior-point method capable of rapidly detecting infeasibility for nonlinear programs
Authors: Dai, Y.-H.; Liu, X.-W.; Sun, J.
Abstract: With the help of a logarithmic barrier augmented Lagrangian function, we can obtain closed-form solutions of slack variables of logarithmicbarrier problems of nonlinear programs. As a result, a two-parameter primaldual nonlinear system is proposed, which corresponds to the Karush-Kuhn-Tucker point and the infeasible stationary point of nonlinear programs, respectively, as one of two parameters vanishes. Based on this distinctive system, we present a primal-dual interior-point method capable of rapidly detecting infeasibility of nonlinear programs. The method generates interior-point iterates without truncation of the step. It is proved that our method converges to a Karush-Kuhn-Tucker point of the original problem as the barrier parameter tends to zero. Otherwise, the scaling parameter tends to zero, and the method converges to either an infeasible stationary point or a singular stationary point of the original problem. Moreover, our method has the capability to rapidly detect the infeasibility of the problem. Under suitable conditions, the method can be superlinearly or quadratically convergent to the Karush-Kuhn-Tucker point if the original problem is feasible, and it can be superlinearly or quadratically convergent to the infeasible stationary point when the problem is infeasible. Preliminary numerical results show that the method is ecient in solving some simple but hard problems, where the superlinear convergence to an infeasible stationary point is demonstrated when we solve two infeasible problems in the literature. © 2020, American Institute of Mathematical Sciences.
Wed, 01 Jan 2020 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1961922020-01-01T00:00:00Z
- Establishing Nash equilibrium of the manufacturer-supplier game in supply chain managementhttps://scholarbank.nus.edu.sg/handle/10635/116721Title: Establishing Nash equilibrium of the manufacturer-supplier game in supply chain management
Authors: Ang, J.; Fukushima, M.; Meng, F.; Noda, T.; Sun, J.
Abstract: We study a game model of multi-leader and one-follower in supply chain optimization where n suppliers compete to provide a single product for a manufacturer. We regard the selling price of each supplier as a pre-determined parameter and consider the case that suppliers compete on the basis of delivery frequency to the manufacturer. Each supplier's profit depends not only on its own delivery frequency, but also on other suppliers' frequencies through their impact on manufacturer's purchase allocation to the suppliers. We first solve the follower's (manufacturer's) purchase allocation problem by deducing an explicit formula of its solution. We then formulate the n leaders' (suppliers') game as a generalized Nash game with shared constraints, which is theoretically difficult, but in our case could be solved numerically by converting to a regular variational inequality problem. For the special case that the selling prices of all suppliers are identical, we provide a sufficient and necessary condition for the existence and uniqueness of the Nash equilibrium. An explicit formula of the Nash equilibrium is obtained and its local uniqueness property is proved. © 2012 Springer Science+Business Media, LLC.
Thu, 01 Aug 2013 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1167212013-08-01T00:00:00Z
- A robust primal-dual interior-point algorithm for nonlinear programshttps://scholarbank.nus.edu.sg/handle/10635/44231Title: A robust primal-dual interior-point algorithm for nonlinear programs
Authors: Liu, X.; Sun, J.
Abstract: We present a primal-dual interior-point algorithm for solving optimization problems with nonlinear inequality constraints. The algorithm has some of the theoretical properties of trust region methods, but works entirely by line search. Global convergence properties are derived without assuming regularity conditions. The penalty parameter p in the merit function is updated adaptively and plays two roles in the algorithm. First, it guarantees that the search directions are descent directions of the updated merit function. Second, it helps to determine a suitable search direction in a decomposed SQP step. It is shown that if ρ is bounded for each barrier parameter μ, then every limit point of the sequence generated by the algorithm is a Karush Kuhn-Tucker point, whereas if ρ is unbounded for some μ, then the sequence has a limit point which is either a Fritz-John point or a stationary point of a function measuring the violation of the constraints. Numerical results confirm that the algorithm produces the correct results for some hard problems, including the example provided by Wächter and Biegler, for which many of the existing line search-based interior-point methods have failed to find the right answers.
Thu, 01 Jan 2004 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/442312004-01-01T00:00:00Z
- An alternating direction method for solving convex nonlinear semidefinite programming problemshttps://scholarbank.nus.edu.sg/handle/10635/116218Title: An alternating direction method for solving convex nonlinear semidefinite programming problems
Authors: Zhang, S.; Ang, J.; Sun, J.
Abstract: An alternating direction method is proposed for solving convex semidefinite optimization problems. This method only computes several metric projections at each iteration. Convergence analysis is presented and numerical experiments in solving matrix completion problems are reported. © 2013 Copyright Taylor and Francis Group, LLC.
Mon, 01 Apr 2013 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1162182013-04-01T00:00:00Z
- A smoothing Newton algorithm for the LCP with a sufficient matrix that terminates finitely at a maximally complementary solutionhttps://scholarbank.nus.edu.sg/handle/10635/44134Title: A smoothing Newton algorithm for the LCP with a sufficient matrix that terminates finitely at a maximally complementary solution
Authors: Sun, J.; Huang, Z.-H.
Abstract: By using a smoothing function, the linear complementarity problem (LCP) can be reformulated as a parameterized smooth equation. A Newton method with a projection-type testing procedure is proposed to solve this equation. We show that, for the LCP with a sufficient matrix, the iteration sequence generated by the proposed algorithm is bounded as long as the LCP has a solution. This assumption is weaker than the ones used in most existing smoothing algorithms. Moreover, we show that the proposed algorithm can find a maximally complementary solution to the LCP in a finite number of iterations.
Sun, 01 Jan 2006 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/441342006-01-01T00:00:00Z
- Analysis of third-party warehousing contracts with commitmentshttps://scholarbank.nus.edu.sg/handle/10635/44969Title: Analysis of third-party warehousing contracts with commitments
Authors: Chen, F.Y.; Hum, S.H.; Sun, J.
Abstract: This paper considers multi-period warehousing contracts under random space demand. A typical contract is specified by a starting space commitment plus a certain number of times at which the commitment can be further modified. Three forms of contracts are analysed: (1) there is a restriction on the range of commitment changes and the schedule for the changes is preset by the warehouser; (2) the same as form (1) but there is no restriction on the range; (3) the same as form (2) but the schedule for the changes is chosen by the user. We explore properties and algorithms for the three problems from the user's perspective. Solutions of simple form are obtained for the first two models and an efficient dynamic programming (DP) procedure is proposed for the last. A numerical comparison of the total expected leasing costs suggests that under certain demand patterns, contract forms (2) and (3) could be cost effective. © 2001 Elsevier Science B.V.
Mon, 01 Jan 2001 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/449692001-01-01T00:00:00Z
- Global convergence analysis of line search interior-point methods for nonlinear programming without regularity assumptionshttps://scholarbank.nus.edu.sg/handle/10635/44227Title: Global convergence analysis of line search interior-point methods for nonlinear programming without regularity assumptions
Authors: Liu, X.W.; Sun, J.
Abstract: As noted by Wächter and Biegler (Ref. 1), a number of interior-point methods for nonlinear programming based on line-search strategy may generate a sequence converging to an infeasible point. We show that, by adopting a suitable merit function, a modified primal-dual equation, and a proper line-search procedure, a class of interior-point methods of line-search type will generate a sequence such that either all the limit points of the sequence are KKT points, or one of the limit points is a Fritz John point, or one of the limit points is an infeasible point that is a stationary point minimizing a function measuring the extent of violation to the constraint system. The analysis does not depend on the regularity assumptions on the problem. Instead, it uses a set of satisfiable conditions on the algorithm implementation to derive the desired convergence property. © 2005 Springer Science+Business Media, Inc.
Sat, 01 Jan 2005 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/442272005-01-01T00:00:00Z
- Second-order sufficient conditions for error bounds in banach spaceshttps://scholarbank.nus.edu.sg/handle/10635/44037Title: Second-order sufficient conditions for error bounds in banach spaces
Authors: He, Y.; Sun, J.
Abstract: Recently, Huang and Ng presented second-order sufficient conditions for error bounds of continuous and Gâteaux differentiate functions in Banach spaces. Wu and Ye dropped the assumption of Huang and Ng on Gâteaux differentiability but required the space to be a Hilbert space. We carry on this research in two directions. First we extend Wu and Ye's result to some non-Hilbert spaces; second, same as Huang and Ng, we work on Banach spaces but provide different second-order sufficient conditions that may allow the function to be non-Gâteaux differentiate. © 2006 Society for Industrial and Applied Mathematics.
Sun, 01 Jan 2006 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/440372006-01-01T00:00:00Z
- A distributed multi-agent environment for product design and manufacturing planninghttps://scholarbank.nus.edu.sg/handle/10635/45059Title: A distributed multi-agent environment for product design and manufacturing planning
Authors: Sun, J.; Zhang, Y.F.; Nee, A.Y.C.
Abstract: This paper describes a multi-agent approach to the integration of product design, manufacturability analysis, and process planning in a distributed manner. The objective is to develop a distributed concurrent engineering system to allow geographically dispered entities to work cooperatively towards overall system goals. In the paper, an agent-based concurrent engineering system concerning product design and manufacturing planning, and its fundamental framework and functions are presented. The proposed model considers constraints and requirements from the different product development cycles in the early development phases and fully supports the concept of design-for-manufacturability. This methodology uses conflict resolution (CR) techniques and design-improvement suggestions to refine the initial product design. The model comprises a facilitator agent, a console agent and six services agents. Each service agents is used to model different product development phases, and the console agent acts as an interacting interface between designers and the system, while the facilitator is responsible for the decomposition and dispatch of tasks, and resolving conflicts of poor designs. A prototype system for part design, manufacturability analysis, and process planning has been implemented. The performance of the prototype system shows that it could be extended to include other service agents, such as assemblability analysis, to become a comprehensive distributed concurrent engineering system for geographically dispersed customers and suppliers.
Mon, 01 Jan 2001 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/450592001-01-01T00:00:00Z
- Global convergence of nonmonotone descent methods for unconstrained optimization problemshttps://scholarbank.nus.edu.sg/handle/10635/43973Title: Global convergence of nonmonotone descent methods for unconstrained optimization problems
Authors: Sun, W.; Han, J.; Sun, J.
Abstract: Global convergence results are established for unconstrained optimization algorithms that utilize a nonmonotone line search procedure. This procedure allows the user to specify a flexible forcing function and includes the nonmonotone Armijo rule, the nonmonotone Goldstein rule, and the nonmonotone Wolfe rule as special cases. © 2002 Elsevier Science B.V. All rights reserved.
Tue, 01 Jan 2002 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/439732002-01-01T00:00:00Z
- Generalized stationary points and an interior-point method for mathematical programs with equilibrium constraintshttps://scholarbank.nus.edu.sg/handle/10635/44247Title: Generalized stationary points and an interior-point method for mathematical programs with equilibrium constraints
Authors: Liu, X.; Sun, J.
Abstract: Generalized stationary points of the mathematical program with equilibrium constraints (MPEC) are studied to better describe the limit points produced by interior point methods for MPEC. A primal-dual interior-point method is then proposed, which solves a sequence of relaxed barrier problems derived from MPEC. Global convergence results are deduced under fairly general conditions other than strict complementarity or the linear independence constraint qualification for MPEC (MPEC-LICQ). It is shown that every limit point of the generated sequence is a strong stationary point of MPEC if the penalty parameter of the merit function is bounded. Otherwise, a point with certain stationarity can be obtained. Preliminary numerical results are reported, which include a case analyzed by Leyffer for which the penalty interior-point algorithm failed to find a stationary point. © Springer-Verlag 2004.
Thu, 01 Jan 2004 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/442472004-01-01T00:00:00Z
- The rate of convergence of the augmented Lagrangian method for nonlinear semidefinite programminghttps://scholarbank.nus.edu.sg/handle/10635/44217Title: The rate of convergence of the augmented Lagrangian method for nonlinear semidefinite programming
Authors: Sun, D.; Sun, J.; Zhang, L.
Abstract: We analyze the rate of local convergence of the augmented Lagrangian method in nonlinear semidefinite optimization. The presence of the positive semidefinite cone constraint requires extensive tools such as the singular value decomposition of matrices, an implicit function theorem for semismooth functions, and variational analysis on the projection operator in the symmetric matrix space. Without requiring strict complementarity, we prove that, under the constraint nondegeneracy condition and the strong second order sufficient condition, the rate of convergence is linear and the ratio constant is proportional to 1/c, where c is the penalty parameter that exceeds a threshold c̄ > 0 . © 2007 Springer-Verlag.
Tue, 01 Jan 2008 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/442172008-01-01T00:00:00Z
- Subdifferential properties of the minimal time function of linear control systemshttps://scholarbank.nus.edu.sg/handle/10635/44051Title: Subdifferential properties of the minimal time function of linear control systems
Authors: Jiang, Y.; He, Y.R.; Sun, J.
Abstract: We present several formulae for the proximal and Fréchet subdifferentials of the minimal time function defined by a linear control system and a target set. At every point inside the target set, the proximal/Fréchet subdifferential is the intersection of the proximal/Fréchet normal cone of the target set and an upper level set of a so-called Hamiltonian function which depends only on the linear control system. At every point outside the target set, under a mild assumption, proximal/Fréchet subdifferential is the intersection of the proximal/Fréchet normal cone of an enlargement of the target set and a level set of the Hamiltonian function. © 2010 Springer Science+Business Media, LLC.
Sat, 01 Jan 2011 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/440512011-01-01T00:00:00Z
- Some properties of the augmented Lagrangian in cone constrained optimizationhttps://scholarbank.nus.edu.sg/handle/10635/44110Title: Some properties of the augmented Lagrangian in cone constrained optimization
Authors: Shapiro, A.; Sun, J.
Abstract: A large class of optimization problems can be modeled as minimization of an objective function subject to constraints given in a form of set inclusions. In this paper, we discuss augmented Lagrangian duality for such optimization problems. We formulate the augmented Lagrangian dual problems and study conditions ensuring existence of the corresponding augmented Lagrange multipliers. We also discuss sensitivity of optimal solutions to small perturbations of augmented Lagrange multipliers. © 2004 INFORMS.
Thu, 01 Jan 2004 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/441102004-01-01T00:00:00Z
- Strong semismoothness of eigenvalues of symmetric matrices and its application to inverse eigenvalue problemshttps://scholarbank.nus.edu.sg/handle/10635/44233Title: Strong semismoothness of eigenvalues of symmetric matrices and its application to inverse eigenvalue problems
Authors: Sun, D.; Sun, J.
Abstract: It is well known that the eigenvalues of a real symmetric matrix are not everywhere differentiable. A classical result of Ky Fan states that each eigenvalue of a symmetric matrix is the difference of two convex functions, which implies that the eigenvalues are semismooth functions. Based on a recent result of the authors, it is further proved in this paper that the eigenvalues of a symmetric matrix are strongly semismooth everywhere. As an application, it is demonstrated how this result can be used to analyze the quadratic convergence of Newton's method for solving inverse eigenvalue problems (IEPs) and generalized IEPs with multiple eigenvalues.
Tue, 01 Jan 2002 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/442332002-01-01T00:00:00Z
- Solving variational inequality problems via smoothing-nonsmooth reformulationshttps://scholarbank.nus.edu.sg/handle/10635/44904Title: Solving variational inequality problems via smoothing-nonsmooth reformulations
Authors: Sun, J.
Abstract: It has long been known that variational inequality problems can be reformulated as nonsmooth equations. Recently, locally high-order convergent Newton methods for nonsmooth equations have been well established via the concept of semismoothness. When the constraint set of the variational inequality problem is a rectangle, several locally convergent Newton methods for the reformulated nonsmooth equations can also be globalized. In this paper, our main aim is to provide globally and locally high-order convergent Newton methods for solving variational inequality problems with general constraints. To achieve this, we first prove via convolution that these nonsmooth equations can be well approximated by smooth equations, which have desirable properties for the design of Newton methods. We then reformulate the variational inequality problems as equivalent smoothing-nonsmooth equations and apply Newton-type methods to solve the latter systems, and so the variational inequality problems. Stronger convergence results have been obtained. © 2001 Elsevier Science B.V. All rights reserved.
Mon, 01 Jan 2001 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/449042001-01-01T00:00:00Z
- A trust region algorithm for minimization of locally Lipschitzian functionshttps://scholarbank.nus.edu.sg/handle/10635/44945Title: A trust region algorithm for minimization of locally Lipschitzian functions
Authors: Qi, L.; Sun, J.
Abstract: The classical trust region algorithm for smooth nonlinear programs is extended to the nonsmooth case where the objective function is only locally Lipschitzian. At each iteration, an objective function that carries both first and second order information is minimized over a trust region. The term that carries the first order information is an iteration function that may not explicitly depend on subgradients or directional derivatives. We prove that the algorithm is globally convergent. This convergence result extends the result of Powell for minimization of smooth functions, the result of Yuan for minimization of composite convex functions, and the result of Dennis, Li and Tapia for minimization of regular functions. In addition, compared with the recent model of Pang, Han and Rangaraj for minimization of locally Lipschitzian functions using a line search, this algorithm has the same convergence property without assuming positive definiteness and uniform boundedness of the second order term. Applications of the algorithm to various nonsmooth optimization problems are discussed. © 1994 The Mathematical Programming Society, Inc.
Sat, 01 Jan 1994 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/449451994-01-01T00:00:00Z
- Properties of the augmented Lagrangian in nonlinear semidefinite optimizationhttps://scholarbank.nus.edu.sg/handle/10635/43962Title: Properties of the augmented Lagrangian in nonlinear semidefinite optimization
Authors: Sun, J.; Zhang, L.W.; Wu, Y.
Abstract: We study the properties of the augmented Lagrangian function for nonlinear semidefinite programming. It is shown that, under a set of sufficient conditions, the augmented Lagrangian algorithm is locally convergent when the penalty parameter is larger than a certain threshold. An error estimate of the solution, depending on the penalty parameter, is also established. © 2006 Springer Science+Business Media, Inc.
Sun, 01 Jan 2006 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/439622006-01-01T00:00:00Z
- A modified alternating direction method for convex quadratically constrained quadratic semidefinite programshttps://scholarbank.nus.edu.sg/handle/10635/44063Title: A modified alternating direction method for convex quadratically constrained quadratic semidefinite programs
Authors: Sun, J.; Zhang, S.
Abstract: We propose a modified alternating direction method for solving convex quadratically constrained quadratic semidefinite optimization problems. The method is a first-order method, therefore requires much less computational effort per iteration than the second-order approaches such as the interior point methods or the smoothing Newton methods. In fact, only a single inexact metric projection onto the positive semidefinite cone is required at each iteration. We prove global convergence and provide numerical evidence to show the effectiveness of this method. © 2010 Elsevier B.V. All rights reserved.
Fri, 01 Jan 2010 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/440632010-01-01T00:00:00Z
- Global convergence of a two-parameter family of conjugate gradient methods without line searchhttps://scholarbank.nus.edu.sg/handle/10635/43972Title: Global convergence of a two-parameter family of conjugate gradient methods without line search
Authors: Chen, X.; Sun, J.
Abstract: We study the global convergence of a two-parameter family of conjugate gradient methods in which the line search procedure is replaced by a fixed formula of stepsize. This character is of significance if the line search is expensive in a particular application. In addition to the convergence results, we present computational results for various conjugate gradient methods without line search including those discussed by Sun and Zhang (Ann. Oper. Res. 103 (2001) 161-173). © 2002 Elsevier Science B.V. All rights reserved.
Tue, 01 Jan 2002 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/439722002-01-01T00:00:00Z
- A predictor-corrector method for extended linear-quadratic programminghttps://scholarbank.nus.edu.sg/handle/10635/44930Title: A predictor-corrector method for extended linear-quadratic programming
Authors: Sun, J.; Zhu, J.
Abstract: The saddle point form of extended linear-quadratic programs can be solved by an interior point path-following method in polynomial time. The algorithm may take advantage of the block structures of certain problems arising from optimal control and stochastic programming. In addition, it needs no line searches and treats fully or not fully quadratic problems equally. Preliminary computational results apparently show that the algorithm is effective in solving a class of two-stage stochastic programming problems. Copyright © 1996 Elsevier Science Ltd.
Mon, 01 Jan 1996 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/449301996-01-01T00:00:00Z
- A note on the Lipschitz continuity of the gradient of the squared norm of the matrix-valued Fischer-Burmeister functionhttps://scholarbank.nus.edu.sg/handle/10635/44039Title: A note on the Lipschitz continuity of the gradient of the squared norm of the matrix-valued Fischer-Burmeister function
Authors: SIM CHEE KHIAN; Sun, J.; Ralph, D.
Abstract: Based on a formula of Tseng, we show that the squared norm of the matrix-valued Fischer-Burmeister function has a Lipschitz continuous gradient.
Sun, 01 Jan 2006 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/440392006-01-01T00:00:00Z
- Optimization Methods and Software: Prefacehttps://scholarbank.nus.edu.sg/handle/10635/44170Title: Optimization Methods and Software: Preface
Authors: Huang, X.; Sun, J.; Yang, X.; Yang, X.
Fri, 01 Jan 2010 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/441702010-01-01T00:00:00Z
- Stochastic Optimization Problems with CVaR Risk Measure and Their Sample Average Approximationhttps://scholarbank.nus.edu.sg/handle/10635/44000Title: Stochastic Optimization Problems with CVaR Risk Measure and Their Sample Average Approximation
Authors: Meng, F.W.; Sun, J.; Goh, M.
Abstract: We provide a refined convergence analysis for the SAA (sample average approximation) method applied to stochastic optimization problems with either single or mixed CVaR (conditional value-at-risk) measures. Under certain regularity conditions, it is shown that any accumulation point of the weak GKKT (generalized Karush-Kuhn-Tucker) points produced by the SAA method is almost surely a weak stationary point of the original CVaR or mixed CVaR optimization problems. In addition, it is shown that, as the sample size increases, the difference of the optimal values between the SAA problems and the original problem tends to zero with probability approaching one exponentially fast. © 2010 Springer Science+Business Media, LLC.
Fri, 01 Jan 2010 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/440002010-01-01T00:00:00Z
- Parallel Interior Point Schemes for Solving Multistage Convex Programminghttps://scholarbank.nus.edu.sg/handle/10635/44918Title: Parallel Interior Point Schemes for Solving Multistage Convex Programming
Authors: Hegland, M.; Osborne, M.R.; Sun, J.
Abstract: The predictor-corrector interior-point path-following algorithm is promising in solving multistage convex programming problems. Among many other general good features of this algorithm, especially attractive is that the algorithm allows possibility to parallelise the major computations. The dynamic structure of the multistage problems specifies a block-tridiagonal system at each Newton step of the algorithm. A wrap-around permutation is then used to implement the parallel computation for this step.
Mon, 01 Jan 2001 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/449182001-01-01T00:00:00Z
- A non-interior continuation algorithm for the P0 or P * LCP with strong global and local convergence propertieshttps://scholarbank.nus.edu.sg/handle/10635/43953Title: A non-interior continuation algorithm for the P0 or P * LCP with strong global and local convergence properties
Authors: Huang, Z.-H.; Sun, J.
Abstract: We propose a non-interior continuation algorithm for the solution of the linear complementarity problem (LCP) with a P0 matrix. The proposed algorithm differentiates itself from the current continuation algorithms by combining good global convergence properties with good local convergence properties under unified conditions. Specifically, it is shown that the proposed algorithm is globally convergent under an assumption which may be satisfied even if the solution set of the LCP is unbounded. Moreover, the algorithm is globally linearly and locally superlinearly convergent under a nonsingularity assumption. If the matrix in the LCP is a P* matrix, then the above results can be strengthened to include global linear and local quadratic convergence under a strict complementary condition without the nonsingularity assumption. © 2005 Springer Science+Business Media, Inc.
Sat, 01 Jan 2005 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/439532005-01-01T00:00:00Z
- On methods for solving nonlinear semidefinite optimization problemshttps://scholarbank.nus.edu.sg/handle/10635/117101Title: On methods for solving nonlinear semidefinite optimization problems
Authors: Sun, J.
Abstract: The nonlinear semidefinite optimization problem arises from applications in system control, structural design, financial management, and other fields. However, much work is yet to be done to effectively solve this problem. We introduce some new theoretical and algorithmic development in this field. In particular, we discuss first and second-order algorithms that appear to be promising, which include the alternating direction method, the augmented Lagrangian method, and the smoothing Newton method. Convergence theorems are presented and preliminary numerical results are reported.
Tue, 01 Feb 2011 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1171012011-02-01T00:00:00Z
- Scenario formulation of stochastic linear programs and the homogeneous self-dual interior-point methodhttps://scholarbank.nus.edu.sg/handle/10635/44074Title: Scenario formulation of stochastic linear programs and the homogeneous self-dual interior-point method
Authors: Sun, J.; Liu, X.
Abstract: We consider a homogeneous self-dual interior-point algorithm for solving multistage stochastic linear programs. The algorithm is particularly suitable for the so-called "scenario formulation" of the problem, whose constraint system consists of a large block-diagonal matrix together with a set of sparse nonanticipativity constraints. Due to this structure, the major computational work required by the homogeneous self-dual interior-point method can be split into three steps, each of which is highly decomposable. Numerical results on some randomly generated problems and a multistage production-planning problem are reported. © 2006 INFORMS.
Sun, 01 Jan 2006 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/440742006-01-01T00:00:00Z
- On the log-exponential trajectory of linear programminghttps://scholarbank.nus.edu.sg/handle/10635/43949Title: On the log-exponential trajectory of linear programming
Authors: Sun, J.; Zhang, L.
Abstract: Development in interior point methods has suggested various solution trajectories, also called central paths, for linear programming. In this paper we define a new central path through a log-exponential perturbation to the complementarity equation in the Karush-Kuhn-Tucker system. The behavior of this central path is investigated and an algorithm is proposed. The algorithm can compute an ε-optimal solution at a superlinear rate of convergence. © 2003 Kluwer Academic Publishers.
Wed, 01 Jan 2003 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/439492003-01-01T00:00:00Z
- Optimal atomic-resolution structures of prion AGAAAAGA amyloid fibrilshttps://scholarbank.nus.edu.sg/handle/10635/43977Title: Optimal atomic-resolution structures of prion AGAAAAGA amyloid fibrils
Authors: Zhang, J.; Sun, J.; Wu, C.
Abstract: X-ray crystallography is a powerful tool to determine the protein 3D structure. However, it is time-consuming and expensive, and not all proteins can be successfully crystallized, particularly for membrane proteins. Although nuclear magnetic resonance (NMR) spectroscopy is indeed a very powerful tool in determining the 3D structures of membrane proteins, it is also time-consuming and costly. To the best of the authors' knowledge, there is little structural data available on the AGAAAAGA palindrome in the hydrophobic region (113-120) of prion proteins due to the noncrystalline and insoluble nature of the amyloid fibril, although many experimental studies have shown that this region has amyloid fibril forming properties and plays an important role in prion diseases. In view of this, the present study is devoted to address this problem from computational approaches such as global energy optimization, simulated annealing, and structural bioinformatics. The optimal atomic-resolution structures of prion AGAAAAGA amyloid fibils reported in this paper have a value to the scientific community in its drive to find treatments for prion diseases. © 2011.
Sat, 01 Jan 2011 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/439772011-01-01T00:00:00Z
- Solution methodologies for the smallest enclosing circle problemhttps://scholarbank.nus.edu.sg/handle/10635/114876Title: Solution methodologies for the smallest enclosing circle problem
Authors: Xu, S.; Freund, R.M.; Sun, J.
Abstract: Given a set of circles C = {c1,..., cn} on the Euclidean plane with centers {(a1, b1),..., (an, bn)} and radii {r1,.... rn}, the smallest enclosing circle (of fixed circles) problem is to find the circle of minimum radius that encloses all circles in C. We survey four known approaches for this problem, including a second order cone reformulation, a subgradient approach, a quadratic programming scheme, and a randomized incremental algorithm. For the last algorithm we also give some implementation details. It turns out the quadratic programming scheme outperforms the other three in our computational experiment.
Tue, 01 Apr 2003 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1148762003-04-01T00:00:00Z