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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 Type of Solution Method for the Generalized Linear Complementarity Problem over a Polyhedral Cone 被引量:2
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作者 Hong-Chun Sun Yan-Liang Dong 《International Journal of Automation and computing》 EI 2009年第3期228-233,共6页
This paper addresses the generalized linear complementarity problem (GLCP) over a polyhedral cone. To solve the problem, we first equivalently convert the problem into an affine variational inequalities problem over... This paper addresses the generalized linear complementarity problem (GLCP) over a polyhedral cone. To solve the problem, we first equivalently convert the problem into an affine variational inequalities problem over a closed polyhedral cone, and then propose a new type of method to solve the GLCP based on the error bound estimation. The global and R-linear convergence rate is established. The numerical experiments show the efficiency of the method. 展开更多
关键词 Generalized linear complementarity problem (GLCP) error bound algorithm global convergence R-linear convergence rate.
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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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EXTENSION OF SMOOTHING FUNCTIONS TO SYMMETRIC CONE COMPLEMENTARITY PROBLEMS 被引量:2
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作者 Liu Yongjin Zhang Liwei Liu Meijiao 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2007年第2期245-252,共8页
The paper uses Euclidean Jordan algebras as a basic tool to extend smoothing functions, which include the Chen-Mangasarian class and the Fischer-Burmeister smoothing functions, to symmetric cone complementarity proble... The paper uses Euclidean Jordan algebras as a basic tool to extend smoothing functions, which include the Chen-Mangasarian class and the Fischer-Burmeister smoothing functions, to symmetric cone complementarity problems. Computable formulas for these functions and their Jacobians are derived. In addition, it is shown that these functions are Lipschitz continuous with respect to parameter # and continuously differentiable on J × J for any μ 〉 0. 展开更多
关键词 symmetric cone complementarity problem smoothing function Euclidean Jordan algebra non-interior continuation method
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A GLOBAL LINEAR AND LOCAL QUADRATIC SINGLE-STEP NONINTERIOR CONTINUATION METHOD FOR MONOTONE SEMIDEFINITE COMPLEMENTARITY PROBLEMS 被引量:1
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作者 张立平 《Acta Mathematica Scientia》 SCIE CSCD 2007年第2期243-253,共11页
A noninterior continuation method is proposed for semidefinite complementarity problem (SDCP). This method improves the noninterior continuation methods recently developed for SDCP by Chen and Tseng. The main proper... A noninterior continuation method is proposed for semidefinite complementarity problem (SDCP). This method improves the noninterior continuation methods recently developed for SDCP by Chen and Tseng. The main properties of our method are: (i) it is well d.efined for the monotones SDCP; (ii) it has to solve just one linear system of equations at each step; (iii) it is shown to be both globally linearly convergent and locally quadratically convergent under suitable assumptions. 展开更多
关键词 Semidefinite complementarity problem noninterior continuation method global convergence local quadratic convergence
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A New Infeasible Interior-point Method for Linear Complementarity Problem Based on Full Newton Step 被引量:1
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作者 龚小玉 胡振鹏 王先甲 《Chinese Quarterly Journal of Mathematics》 CSCD 2012年第4期624-632,共9页
This paper proposes an infeasible interior-point algorithm with full-Newton step for linear complementarity problem,which is an extension of Roos about linear optimization. The main iteration of the algorithm consists... This paper proposes an infeasible interior-point algorithm with full-Newton step for linear complementarity problem,which is an extension of Roos about linear optimization. The main iteration of the algorithm consists of a feasibility step and several centrality steps. At last,we prove that the algorithm has O(nlog n/ε) polynomial complexity,which coincides with the best known one for the infeasible interior-point algorithm at present. 展开更多
关键词 complementarity problem infeasible interior-point methods full-Newton step polynomial complexity
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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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A New Conjugate Gradient Projection Method for Solving Stochastic Generalized Linear Complementarity Problems 被引量:2
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作者 Zhimin Liu Shouqiang Du Ruiying Wang 《Journal of Applied Mathematics and Physics》 2016年第6期1024-1031,共8页
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
关键词 Stochastic Generalized Linear complementarity problems Fischer-Burmeister Function Conjugate Gradient Projection Method Global Convergence
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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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Merit functions for nonsmooth complementarity problems and related descent algorithm
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作者 DU Shou-qiang GAO Yan 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2010年第1期78-84,共7页
Under some assumptions, the solution set of a nonlinear complementarity problem coincides with the set of local minima of the corresponding minimization problem. This paper uses a family of new merit functions to deal... Under some assumptions, the solution set of a nonlinear complementarity problem coincides with the set of local minima of the corresponding minimization problem. This paper uses a family of new merit functions to deal with nonlinear complementarity problem where the underlying function is assumed to be a continuous but not necessarily locally Lipschitzian map and gives a descent algorithm for solving the nonsmooth continuous complementarity problems. In addition, the global convergence of the derivative free descent algorithm is also proved. 展开更多
关键词 Nonsmooth complementarity problem merit function nonsmooth continuous map descent algorithm.
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GLOBAL LINEAR AND QUADRATIC ONE-STEP SMOOTHING NEWTON METHOD FOR VERTICAL LINEAR COMPLEMENTARITY PROBLEMS
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作者 张立平 高自友 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2003年第6期738-746,F003,共10页
A one_step smoothing Newton method is proposed for solving the vertical linear complementarity problem based on the so_called aggregation function. The proposed algorithm has the following good features: (ⅰ) It solve... A one_step smoothing Newton method is proposed for solving the vertical linear complementarity problem based on the so_called aggregation function. The proposed algorithm has the following good features: (ⅰ) It solves only one linear system of equations and does only one line search at each iteration; (ⅱ) It is well_defined for the vertical linear complementarity problem with vertical block P 0 matrix and any accumulation point of iteration sequence is its solution.Moreover, the iteration sequence is bounded for the vertical linear complementarity problem with vertical block P 0+R 0 matrix; (ⅲ) It has both global linear and local quadratic convergence without strict complementarity. Many existing smoothing Newton methods do not have the property (ⅲ). 展开更多
关键词 vertical linear complementarity problems smoothing Newton method global linear convergence quadratic convergence
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New Mehrotra's second order predictor-corrector algorithm for P_*(κ) linear complementarity problems
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作者 Mingwang Zhang Yanli Lu 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2010年第4期705-712,共8页
It has been shown in various papers that most interior-point algorithms for linear optimization and their analysis can be generalized to P_*(κ) linear complementarity problems.This paper presents an extension of t... It has been shown in various papers that most interior-point algorithms for linear optimization and their analysis can be generalized to P_*(κ) linear complementarity problems.This paper presents an extension of the recent variant of Mehrotra's second order algorithm for linear optimijation.It is shown that the iteration-complexity bound of the algorithm is O(4κ + 3)√14κ + 5 nlog(x0)Ts0/ε,which is similar to that of the corresponding algorithm for linear optimization. 展开更多
关键词 linear complementarity problem P_*(κ)-matrix Mehrotra-type predictor-corrector algorithm polynomial complexity.
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A New Class of Complementarity Function and the Boundedness of Its Merit Function for Symmetric Cone Complementarity Problem
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作者 ZHANG Yun-sheng 《Chinese Quarterly Journal of Mathematics》 CSCD 2014年第3期363-372,共10页
In this paper, we introduce a new class of two-parametric penalized function,which includes the penalized minimum function and the penalized Fischer-Burmeister function over symmetric cone complementarity problems. We... In this paper, we introduce a new class of two-parametric penalized function,which includes the penalized minimum function and the penalized Fischer-Burmeister function over symmetric cone complementarity problems. We propose that this class of function is a class of complementarity functions(C-function). Moreover, its merit function has bounded level set under a weak condition. 展开更多
关键词 complementarity problem symmetric cone C-functions R01function BOUNDEDNESS Euclidean Jordan algebra
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Smoothing Newton Algorithm for Solving Generalized Complementarity Problem
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作者 刘晓红 倪铁 《Transactions of Tianjin University》 EI CAS 2010年第1期75-79,共5页
The generalized complementarity problem includes the well-known nonlinear complementarity problem and linear complementarity problem as special cases.In this paper, based on a class of smoothing functions, a smoothing... The generalized complementarity problem includes the well-known nonlinear complementarity problem and linear complementarity problem as special cases.In this paper, based on a class of smoothing functions, a smoothing Newton-type algorithm is proposed for solving the generalized complementarity problem.Under suitable assumptions, the proposed algorithm is well-defined and global convergent. 展开更多
关键词 generalized complementarity problem smoothing Newton algorithm NCP function global convergence
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Interior-point algorithm based on general kernel function for monotone linear complementarity problem
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作者 刘勇 白延琴 《Journal of Shanghai University(English Edition)》 CAS 2009年第2期95-101,共7页
A polynomial interior-point algorithm is presented for monotone linear complementarity problem (MLCP) based on a class of kernel functions with the general barrier term, which are called general kernel functions. Un... A polynomial interior-point algorithm is presented for monotone linear complementarity problem (MLCP) based on a class of kernel functions with the general barrier term, which are called general kernel functions. Under the mild conditions for the barrier term, the complexity bound of algorithm in terms of such kernel function and its derivatives is obtained. The approach is actually an extension of the existing work which only used the specific kernel functions for the MLCP. 展开更多
关键词 monotone linear complementarity problem (MLCP) interior-point method kernel function polynomial complexity
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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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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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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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A New Generalized FB Complementarity Function for Symmetric Cone Complementarity Problems
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作者 ZHANG YUN-SHENG GAO LEI-FU 《Communications in Mathematical Research》 CSCD 2016年第1期39-46,共8页
We establish that the generalized Fischer-Burmeister(FB) function and penalized Generalized Fischer-Burmeister (FB) function defined on symmetric cones are complementarity functions (C-functions), in terms of Eu... We establish that the generalized Fischer-Burmeister(FB) function and penalized Generalized Fischer-Burmeister (FB) function defined on symmetric cones are complementarity functions (C-functions), in terms of Euclidean Jordan algebras, and the Generalized Fischer-Burmeister complementarity function for the symmetric cone complementarity problem (SCCP). It provides an affirmative answer to the open question by Kum and Lim (Kum S H, Lim Y. Penalized complementarity functions on symmetric cones. J. Glob. Optim.. 2010, 46: 475-485) for any positive integer. 展开更多
关键词 complementarity problem complementarity function symmetric cone generalized Fischer-Burmeister function
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CONVERGENCE OF A MODIFIED SLP ALGORITHM FOR THE EXTENDED LINEAR COMPLEMENTARITY PROBLEM
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作者 XIU Naihua(修乃华) +1 位作者 GAO Ziyou(高自友) 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2001年第5期602-608,共7页
A modified sequential linear programming algorithm is presented, whose subproblem is always solvable, for the extended linear complementarity problem (XLCP), the global convergence of the algorithm under assumption of... A modified sequential linear programming algorithm is presented, whose subproblem is always solvable, for the extended linear complementarity problem (XLCP), the global convergence of the algorithm under assumption of X-row sufficiency or X-colunm monotonicity is proved. As a result, a sufficient condition for existence and boundedness of solution to the XLCP are obtained. 展开更多
关键词 extended linear complementarity problem modified SLP algorithm global convergence
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