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Smoothing Newton Algorithm for Nonlinear Complementarity Problem with a PFunction
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作者 刘丹红 黄涛 王萍 《Transactions of Tianjin University》 EI CAS 2007年第5期379-386,共8页
By using a smoothing function,the P nonlinear complementarity problem(P NCP)can be reformulated as a parameterized smooth equation.A Newton method is proposed to solve this equation.The iteration sequence generated by... By using a smoothing function,the P nonlinear complementarity problem(P NCP)can be reformulated as a parameterized smooth equation.A Newton method is proposed to solve this equation.The iteration sequence generated by the proposed algorithm is bounded and this algorithm is proved to be globally convergent under an assumption that the P NCP has a nonempty solution set.This assumption is weaker than the ones used in most existing smoothing algorithms.In particular,the solution obtained by the proposed algorithm is shown to be a maximally complementary solution of the P NCP without any additional assumption. 展开更多
关键词 p.nonlinear complementarity problem smoothing Newton algorithm maximally complementary solution
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Projection and Contraction Methods for Nonlinear Complementarity Problem 被引量:2
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作者 Zhao She-feng, Fei Pu-sheng College of Mathematics and Computer Science,Wuhan University,Wuhan 430072,China 《Wuhan University Journal of Natural Sciences》 EI CAS 2000年第4期391-396,共6页
We applied the projection and contraction method to nonlinear complementarity problem (NCP). Moveover, we proposed an inexact implicit method for (NCP) and proved the convergence.
关键词 nonlinear complementarity problem projection and contraction method implicit method
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Trust Region Algorithm for a Class of Nonlinear Complementarity Problem 被引量:3
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作者 OU Yi-gui 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2007年第4期558-566,共9页
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
关键词 nonlinear complementarity problems ODE methods trust region methods Fischer-Burmeister function
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A New Homotopy Method for Nonlinear Complementarity Problems 被引量:6
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作者 Jundi Ding Hongyou Yin 《Numerical Mathematics A Journal of Chinese Universities(English Series)》 SCIE 2007年第2期155-163,共9页
In this paper, we present a new homotopy method for the nonlinear complementarity problems. Without the regularity or non-singulary assumptions for▽F(x), we prove that our homotopy equations have a bounded solution c... In this paper, we present a new homotopy method for the nonlinear complementarity problems. Without the regularity or non-singulary assumptions for▽F(x), we prove that our homotopy equations have a bounded solution curve. The numerical tests confirm the efficiency of our proposed method. 展开更多
关键词 非线性互补问题 同伦法 有界解 同伦方程
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The Successive Approximation Broyden-like Algorithm for Nonlinear Complementarity Problems 被引量:1
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作者 MAChang-feng LIANGGuo-ping 《Chinese Quarterly Journal of Mathematics》 CSCD 2003年第2期146-153,共8页
In this paper, we present a new form of successive approximation Broyden-like algorithm for nonlinear complementarity problem based on its equivalent nonsmooth equations. Under suitable conditions, we get the global c... In this paper, we present a new form of successive approximation Broyden-like algorithm for nonlinear complementarity problem based on its equivalent nonsmooth equations. Under suitable conditions, we get the global convergence on the algorithms. Some numerical results are also reported. 展开更多
关键词 nonlinear complementarity problem successive approximation Broyden-like algorithm global convergence
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Generalized Strongly Nonlinear Quasi-Complementarity Problems 被引量:2
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作者 李红梅 丁协平 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1994年第4期307-315,共9页
Using the algorithm in this paper, we prove the existence of solutions to the gene-ralized strongly nonlinear quasi-complementarity problems and the convergence of theiterative sequences generated by the algorithm. Ou... Using the algorithm in this paper, we prove the existence of solutions to the gene-ralized strongly nonlinear quasi-complementarity problems and the convergence of theiterative sequences generated by the algorithm. Our results improve and extend thecorresponding results of Noor and Chang-Huang. Moreover, a more general iterativealgorithm for finding the approximate solution of generalized strongly nonlinear quasi-complementarity problems is also given. It is shown that the approximate solution ob-tained by the iterative scheme converges to the exact solution of this quasi-com-plementarity problem. 展开更多
关键词 generalized strongly nonlinear quasi-complementarity problem Hilbert space cone. H-Lipschitz continuous mapping with re-spect to g ψ-strongly monotone mapping with respect to g
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A POSITIVE INTERIOR-POINT ALGORITHM FOR NONLINEAR COMPLEMENTARITY PROBLEMS
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作者 马昌凤 梁国平 陈新美 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2003年第3期355-362,共8页
A new iterative method,which is called positive interior-point algorithm,is presented for solving the nonlinear complementarity problems.This method is of the desirable feature of robustness.And the convergence theore... A new iterative method,which is called positive interior-point algorithm,is presented for solving the nonlinear complementarity problems.This method is of the desirable feature of robustness.And the convergence theorems of the algorithm is established.In addition,some numerical results are reported. 展开更多
关键词 nonlinear complementarity problems positive interior-point algorithm non-smooth equations
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INEXACT DAMPED NEWTON METHOD FOR NONLINEAR COMPLEMENTARITY PROBLEMS
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作者 Li Donghui 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 1996年第4期487-496,共10页
In this paper, we propose an inexact damped Newtonmethod for solving nonlinear complementarity problems based on the equivalent B differentiable equations.Global convergence and locally quadratic convergence are ... In this paper, we propose an inexact damped Newtonmethod for solving nonlinear complementarity problems based on the equivalent B differentiable equations.Global convergence and locally quadratic convergence are obtained,and numerical results are given. 展开更多
关键词 Nonlinear complementarity problems Newton’s method global convergence
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A Singular Values Based Newton Method for Linear Complementarity Problems
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作者 Haishan Han Yuan Li 《Applied Mathematics》 2015年第14期2354-2359,共6页
The existence condition of the solution of special nonlinear penalized equation of the linear complementarity problems is obtained by the relationship between penalized equations and an absolute value equation. Newton... The existence condition of the solution of special nonlinear penalized equation of the linear complementarity problems is obtained by the relationship between penalized equations and an absolute value equation. Newton method is used to solve penalized equation, and then the solution of the linear complementarity problems is obtained. We show that the proposed method is globally and superlinearly convergent when the matrix of complementarity problems of its singular values exceeds 0;numerical results show that our proposed method is very effective and efficient. 展开更多
关键词 Linear complementarity problem Nonlinear Penalized EQUATION NEWTON Method SINGULAR VALUES
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An Existence Theorem for Strongly Nonlinear Implicit Complementarity Problems
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作者 丁体明 《Journal of Chongqing University》 CAS 2002年第1期74-76,共3页
A class of strongly nonlinear implicit complementarity problems for set-valued mappings in Hilbert spaces is studied,Thereupon a new existence theorem is established and proved to be a solution to that kind of problems.
关键词 Nonlinear implicit complementarity problem Set-valued mapping PROJECTION Fixed point
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On the Solution of the Eigenvalue Complementarity Problem by a Line Search Filter-SQP Algorithm
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作者 Qiu Yu Zhensheng Yu Yangchen Liu 《Journal of Applied Mathematics and Physics》 2017年第10期1986-1996,共11页
In this paper, the Eigenvalue Complementarity Problem (EiCP) with real symmetric matrices is addressed, which appears in the study of contact problem in mechanics. We discuss a quadratic programming formulation to the... In this paper, the Eigenvalue Complementarity Problem (EiCP) with real symmetric matrices is addressed, which appears in the study of contact problem in mechanics. We discuss a quadratic programming formulation to the problem. The resulting problems are nonlinear programs that can be solved by a line search filter-SQP algorithm. 展开更多
关键词 EIGENVALUE complementarity problem Nonlinear PROGRAMMING LINE SEARCH FILTER Method
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Some Properties of Solution to Semidefinite Complementarity Problem
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作者 Yu Chen Cuiling Chen Caihong Han 《Journal of Applied Mathematics and Physics》 2018年第1期122-129,共8页
In this paper, we discuss the nonemptyness and boundedness of the solution set for P*-semidefinite complementarity problem by using the concept of exceptional family of elements for complementarity problems over the c... In this paper, we discuss the nonemptyness and boundedness of the solution set for P*-semidefinite complementarity problem by using the concept of exceptional family of elements for complementarity problems over the cone of semidefinite matrices, and obtain a main result that if the corresponding problem has a strict feasible point, then its solution set is nonemptyness and boundedness. 展开更多
关键词 SEMIDEFINITE complementarity problem P*-Mapping Nonemptyness BOUNDEDNESS
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Filter-sequence of quadratic programming method with nonlinear complementarity problem function
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作者 金中 濮定国 +1 位作者 张宇 蔡力 《Journal of Shanghai University(English Edition)》 CAS 2008年第2期97-101,共5页
A mechanism for proving global convergence in filter-SQP (sequence of quadratic programming) method with the nonlinear complementarity problem (NCP) function is described for constrained nonlinear optimization pro... A mechanism for proving global convergence in filter-SQP (sequence of quadratic programming) method with the nonlinear complementarity problem (NCP) function is described for constrained nonlinear optimization problem.We introduce an NCP function into the filter and construct a new SQP-filter algorithm.Such methods are characterized by their use of the dominance concept of multi-objective optimization,instead of a penalty parameter whose adjustment can be problematic.We prove that the algorithm has global convergence and superlinear convergence rates under some mild conditions. 展开更多
关键词 nonlinear complementarity problem (NCP) function FILTER sequence of quadratic programming (SQP) globalconvergence.
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Existence of Solutions for Nonlinear Implicit Complementarity Problems in Reflexive Banach Spaces
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作者 曾六川 《Chinese Quarterly Journal of Mathematics》 CSCD 1997年第1期81-86, ,共6页
In this paper,we prove existence results of soutions for the nonlinear implicit complementarity problems NICP(T,S,K) where K is a closed weakly locally compact convex cone in a reflexive Banach space E,T is a nonlinea... In this paper,we prove existence results of soutions for the nonlinear implicit complementarity problems NICP(T,S,K) where K is a closed weakly locally compact convex cone in a reflexive Banach space E,T is a nonlinear operator from K into E* (i. e.,the dual space of E) and S is a nonlinear operator from K into E. Our results are the essential improvements and extension of the results obtained previously by several authors including Thera,Ding,and Zeng. 展开更多
关键词 nonlinear implicit complementarity problem closed weakly locally compact convex cone sequentially weakly lower semicontinuous
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An Interval Matrix Based Generalized Newton Method for Linear Complementarity Problems
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作者 Hai-Shan Han Lan-Ying   《Open Journal of Applied Sciences》 2015年第8期443-449,共7页
The penalty equation of LCP is transformed into the absolute value equation, and then the existence of solutions for the penalty equation is proved by the regularity of the interval matrix. We propose a generalized Ne... The penalty equation of LCP is transformed into the absolute value equation, and then the existence of solutions for the penalty equation is proved by the regularity of the interval matrix. We propose a generalized Newton method for solving the linear complementarity problem with the regular interval matrix based on the nonlinear penalized equation. Further, we prove that this method is convergent. Numerical experiments are presented to show that the generalized Newton method is effective. 展开更多
关键词 Linear complementarity problem Nonlinear Penalized EQUATION INTERVAL MATRIX GENERALIZED NEWTON Method
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Modulus-Based Multisplitting Iteration Method for a Class of Weakly Nonlinear Complementarity Problem
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作者 Guangbin Wang Fuping Tan 《Communications on Applied Mathematics and Computation》 2021年第3期419-427,共9页
In this paper,we present a modulus-based multisplitting iteration method based on multisplitting of the system matrix for a class of weakly nonlinear complementarity problem.And we prove the convergence of the method ... In this paper,we present a modulus-based multisplitting iteration method based on multisplitting of the system matrix for a class of weakly nonlinear complementarity problem.And we prove the convergence of the method when the system matrix is an H_(+)-matrix.Finally,we give two numerical examples. 展开更多
关键词 Modulus-based multisplitting method Nonlinear complementarity problem H-MATRIX
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A NUMERICAL EMBEDDING METHOD FOR SOLVING THE NONLINEAR COMPLEMENTARITY PROBLEM(Ⅱ)-ALGORITHM AND ITS CONVERGENCE
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作者 张建军 王德人 《Numerical Mathematics A Journal of Chinese Universities(English Series)》 SCIE 2004年第1期94-105,共12页
In this paper, based on the resuls presented in part I of this paper[18],we present a numerical crabeding algorithm for soling the nonlinear complementarity problem, and prove its convergence carefully. Numerical expe... In this paper, based on the resuls presented in part I of this paper[18],we present a numerical crabeding algorithm for soling the nonlinear complementarity problem, and prove its convergence carefully. Numerical experiments show that the algorithm is successful. 展开更多
关键词 数值嵌入 非线性补充问题 收敛性 B-微分方程 P-矩阵
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A Potential-Reduction Algorithm for Linear Complementarity Problems
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作者 WangYan-jin FeiPu-sheng YanZi-zong 《Wuhan University Journal of Natural Sciences》 CAS 2004年第2期144-148,共5页
Feasible-interior-point algorithms start from a strictly feasible interior point, but infeassible-interior-point algorithms just need to start from an arbitrary positive point, we give a potential reduction algorithm ... Feasible-interior-point algorithms start from a strictly feasible interior point, but infeassible-interior-point algorithms just need to start from an arbitrary positive point, we give a potential reduction algorithm from an infeasible-starting-point for a class of non-monotone linear complementarity problem. Its polynomial complexity is analyzed. After finite iterations the algorithm produces an approximate solution of the problem or shows that there is no feasible optimal solution in a large region. Key words linear complementarity problems - infeasible-starting-point - P-matrix - potential function CLC number O 221 Foundation item: Supported by the National Natural Science Foundation of China (70371032) and the Doctoral Educational Foundation of China of the Ministry of Education (20020486035)Biography: Wang Yan-jin (1976-), male, Ph. D candidate, research direction: optimal theory and method. 展开更多
关键词 linear complementarity problems infeasible-starting-point P-MATRIX potential function
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A Direct Algorithm for the Vertical Generalized Complementarity Problem Associated with <i>P</i>-Matrices
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作者 Aniekan Ebiefung George Habetler +1 位作者 Michael Kostreva Bohdan Szanc 《Open Journal of Optimization》 2017年第3期101-114,共14页
We present a direct algorithm for solving the vertical generalized linear complementarity problem, first considered by Cottle and Dantzig, when the associated matrix is a vertical block P-matrix. The algorithm converg... We present a direct algorithm for solving the vertical generalized linear complementarity problem, first considered by Cottle and Dantzig, when the associated matrix is a vertical block P-matrix. The algorithm converges to a unique solution in a finite number of steps, without an assumption of nondegeneracy on the given problem. The algorithm is simple, efficient, and easy to implement. 展开更多
关键词 complementarity problems P-MATRIX Direct Algorithms Linear PROGRAMMING Bi-Matrix GAME
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A SQP METHOD FOR GENERAL NONLINEAR COMPLEMENTARITY PROBLEMS
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作者 Xiu Naihua.Dept.of Appl.Math.,Northern Jiaotong Univ.,Beijing 100044. Email:nhxiu@center.njtu.edu.cn 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2000年第4期433-442,共10页
In this paper,the nonlinear complementarity problem is transformed into the least squares problem with nonnegative constraints,and a SQP algorithm for this reformulation based on a damped Gauss Newton type method is ... In this paper,the nonlinear complementarity problem is transformed into the least squares problem with nonnegative constraints,and a SQP algorithm for this reformulation based on a damped Gauss Newton type method is presented.It is shown that the algorithm is globally and locally superlinearly (quadratically) convergent without the assumption of monotonicity. 展开更多
关键词 Nonlinear complementarity problem SQP method superlinear convergence quadratic convergence.
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