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A SMOOTHING CONJUGATE GRADIENT ALGORITHM FOR NONLINEAR COMPLEMENTARITY PROBLEMS

Journal of Systems Science and Systems Engineering 2008年第4期17卷 460-472页

作者： Caiying WU Guoqing CHEN College of Mathematics Science Inner Mongolia University Hohhot 010021 China

A PRP-type smoothing conjugate gradient method for solving large scale nonlinear complementarity problems （NCP（F）） is proposed. At each iteration, two Armijo line searches are performed, which guarantees the positive property of the smoothing parameter and minimizes the merit function formed by fischer-burmeister function, respectively. Global convergence is studied when F：R^n→R^n is a continuously differentiable P0 ＋ R0 function. Numerical results show that the method is efficient.

关键词： Nonlinear complementarity conjugate gradient global convergence fischer-burmeister function

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SOLVING A CLASS OF INVERSE QP PROBLEMS BY A SMOOTHING NEWTON METHOD

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Journal of Computational Mathematics 2009年第6期27卷 787-801页

作者： Xiantao Xiao Liwei Zhang Department of Applied Mathematics Dalian University of Technology Dalian 116024 China

We consider an inverse quadratic programming （IQP） problem in which the parameters in the objective function of a given quadratic programming （QP） problem are adjusted as little as possible so that a known feasible solution becomes the optimal one. This problem can be formulated as a minimization problem with a positive semidefinite cone constraint and its dual （denoted IQD（A, b）） is a semismoothly differentiable （SC^1） convex programming problem with fewer variables than the original one. In this paper a smoothing Newton method is used for getting a Karush-Kuhn-Tucker point of IQD（A, b）. The proposed method needs to solve only one linear system per iteration and achieves quadratic convergence. Numerical experiments are reported to show that the smoothing Newton method is effective for solving this class of inverse quadratic programming problems.

关键词： fischer-burmeister function Smoothing Newton method Inverse optimization Quadratic programming Convergence rate.

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Trust Region Algorithm for a Class of Nonlinear Complementarity Problem

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Chinese Quarterly Journal of Mathematics 2007年第4期22卷 558-566页

作者： OU Yi-gui Department of Mathematics Hainan University Haikou 570228 China

In this paper, an ODE-type trust region algorithm for solving a class of nonlinear complementarity problems is proposed. A feature of this algorithm is that only the solution of linear systems of equations is required at each iteration, thus avoiding the need for solving a quadratic subproblem with a trust region bound. Under some conditions, it is proven that this algorithm is globally and locally superlinear convergent. The limited numerical examples show its efficiency.

关键词： nonlinear complementarity problems ODE methods trust region methods fischer-burmeister function

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A New Conjugate Gradient Projection Method for Solving Stochastic Generalized Linear Complementarity Problems

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Journal of Applied Mathematics and Physics 2016年第6期4卷 1024-1031页

作者： Zhimin Liu Shouqiang Du Ruiying Wang College of Mathematics and Statistics Qingdao University Qingdao China

In this paper, a class of the stochastic generalized linear complementarity problems with finitely many elements is proposed for the first time. Based on the fischer-burmeister function, a new conjugate gradient projection method is given for solving the stochastic generalized linear complementarity problems. The global convergence of the conjugate gradient projection method is proved and the related numerical results are also reported.

关键词： Stochastic Generalized Linear Complementarity Problems fischer-burmeister function Conjugate Gradient Projection Method Global Convergence

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