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...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.展开更多
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 posit...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.展开更多
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 feasibl...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.展开更多
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 proje...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.展开更多
For the variational inequality with symmetric cone constraints problem,we consider using the inexact modified Newton method to efficiently solve it.It provides a unified framework for dealing with the variational ineq...For the variational inequality with symmetric cone constraints problem,we consider using the inexact modified Newton method to efficiently solve it.It provides a unified framework for dealing with the variational inequality with nonlinear constraints,variational inequality with the second-order cone constraints,and the variational inequality with semi-definite cone constraints.We show that each stationary point of the unconstrained minimization reformulation based on the Fischer-Burmeister merit function is a solution to the problem.It is proved that the proposed algorithm is globally convergent under suitable conditions.The computation results show that the feasibility and efficiency of our algorithm.展开更多
基金Supported by the Natural Science Foundation of Hainan Province(80552)
文摘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.
基金supported by the Teaching and Research Award Program for the Outstanding Young Teachers in Higher Education Institutes of Ministry of Education,P.R.China.
文摘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.
基金supported by the National Natural Science Foundation of China under project No. 10771026by the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry of China
文摘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.
文摘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.
基金supported by the National Natural Science Foundation of China(Nos.11701061,11801503)the Doctoral Fund of Liaoning Province(Nos.20170520373)the Huzhou Science and Technology Plan(Nos.2016GY03)
文摘For the variational inequality with symmetric cone constraints problem,we consider using the inexact modified Newton method to efficiently solve it.It provides a unified framework for dealing with the variational inequality with nonlinear constraints,variational inequality with the second-order cone constraints,and the variational inequality with semi-definite cone constraints.We show that each stationary point of the unconstrained minimization reformulation based on the Fischer-Burmeister merit function is a solution to the problem.It is proved that the proposed algorithm is globally convergent under suitable conditions.The computation results show that the feasibility and efficiency of our algorithm.
