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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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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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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 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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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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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 New Successive Approximation Damped Newton Method for Nonlinear Complementarity Problems 被引量:1
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作者 马昌凤 梁国平 《Journal of Mathematical Research and Exposition》 CSCD 北大核心 2003年第1期1-6,共6页
In this paper, we present a new successive approximation damped Newton method for the nonlinear complementarity problem based on its equivalent nonsmooth equations. Under suitable conditions, we obtain the global conv... In this paper, we present a new successive approximation damped Newton method for the nonlinear complementarity problem based on its equivalent nonsmooth equations. Under suitable conditions, we obtain the global convergence result of the proposed algorithms. Some numerical results are also reported. 展开更多
关键词 nonlinear complementarity problems successive approximation damped Newton method global convergence.
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The non-interior continuation methods for solving the function nonlinear complementarity problem 被引量:17
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作者 黄正海 韩继业 +1 位作者 徐大川 张立平 《Science China Mathematics》 SCIE 2001年第9期1107-1114,共8页
In this paper, we propose a new smooth function that possesses a property not satisfied by the existing smooth functions. Based on this smooth function, we discuss the existence and continuity of the smoothing path fo... In this paper, we propose a new smooth function that possesses a property not satisfied by the existing smooth functions. Based on this smooth function, we discuss the existence and continuity of the smoothing path for solving the P0 function nonlinear complementarity problem (NCP). Using the characteristics of the new smooth function, we investigate the boundedness of the iteration sequence generated by the non-interior continuation methods for solving the P0 function NCP under the assumption that the solution set of the NCP is nonempty and bounded. We show that the assumption that the solution set of the NCP is nonempty and bounded is weaker than those required by a few existing continuation methods for solving the NCP. 展开更多
关键词 nonlinear complementarity problem non-interior continuation method P 0 function boundedness of the iteration sequence
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A LQP BASED INTERIOR PREDICTION-CORRECTION METHOD FOR NONLINEAR COMPLEMENTARITY PROBLEMS 被引量:5
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作者 Bing-sheng He Li-zhi Liao Xiao-ming Yuan 《Journal of Computational Mathematics》 SCIE CSCD 2006年第1期33-44,共12页
To solve nonlinear complementarity problems (NCP), at each iteration, the classical proximal point algorithm solves a well-conditioned sub-NCP while the Logarithmic-Quadratic Proximal (LQP) method solves a system ... To solve nonlinear complementarity problems (NCP), at each iteration, the classical proximal point algorithm solves a well-conditioned sub-NCP while the Logarithmic-Quadratic Proximal (LQP) method solves a system of nonlinear equations (LQP system). This paper presents a practical LQP method-based prediction-correction method for NCP. The predictor is obtained via solving the LQP system approximately under significantly relaxed restriction, and the new iterate (the corrector) is computed directly by an explicit formula derived from the original LQP method. The implementations are very easy to be carried out. Global convergence of the method is proved under the same mild assumptions as the original LQP method. Finally, numerical results for traffic equilibrium problems are provided to verify that the method is effective for some practical problems. 展开更多
关键词 Logarithmic-Quadratic proximal method nonlinear complementarity problems Prediction-correction Inexact criterion
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A NEW SMOOTHING EQUATIONS APPROACH TO THE NONLINEAR COMPLEMENTARITY PROBLEMS 被引量:4
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作者 Chang-fengMa Pu-yanNie Guo-pingLiang 《Journal of Computational Mathematics》 SCIE CSCD 2003年第6期747-758,共12页
The nonlinear complementarity problem can be reformulated as a nonsmooth equation. In this paper we propose a new smoothing Newton algorithm for the solution of the nonlinear complementarity problem by constructing a ... The nonlinear complementarity problem can be reformulated as a nonsmooth equation. In this paper we propose a new smoothing Newton algorithm for the solution of the nonlinear complementarity problem by constructing a new smoothing approximation function. Global and local superlinear convergence results of the algorithm are obtained under suitable conditions. Numerical experiments confirm the good theoretical properties of the algorithm. 展开更多
关键词 nonlinear complementarity problem Smoothing Newton method Global convergence Superlinear convergence.
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On the Convergence of Two-Step Modulus-Based Matrix Splitting Iteration Methods for a Restricted Class of Nonlinear Complementarity Problems with H_(+) -Matrices 被引量:2
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作者 Rui Li Yan Wang Junfeng Yin 《Numerical Mathematics(Theory,Methods and Applications)》 SCIE CSCD 2018年第1期128-139,共12页
We propose the two-step modulus-based matrix splitting iteration methods for a class of nonlinear complementarity problems.The corresponding convergence the-ory is established when the system matrix is an H_(+)-matrix... We propose the two-step modulus-based matrix splitting iteration methods for a class of nonlinear complementarity problems.The corresponding convergence the-ory is established when the system matrix is an H_(+)-matrix.Theoretical analysis gives the choice of parameter matrix involved based on the H-compatible splitting of the sys-tem matrix.Moreover,in actual implementation,the choices of iterative parameters for two-step modulus-based accelerated overrelaxation methods are studied.Numeri-cal experiments show that the method is efficient and further verify the convergence theorems. 展开更多
关键词 nonlinear complementarity problems two-step modulus-based matrix splitting meth-ods H_(+)-matrix H-compatible splitting
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A Null Space Approach for Solving Nonlinear Complementarity Problems 被引量:1
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作者 Pu-yan Nie 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2006年第1期9-20,共12页
In this work, null space techniques are employed to tackle nonlinear complementarity problems (NCPs). NCP conditions are transform into a nonlinear programming problem, which is handled by null space algorithms, The... In this work, null space techniques are employed to tackle nonlinear complementarity problems (NCPs). NCP conditions are transform into a nonlinear programming problem, which is handled by null space algorithms, The NCP conditions are divided into two groups, Some equalities and inequalities in an NCP are treated as constraints, While other equalities and inequalities in an NCP are to be regarded as objective function. Two groups are all updated in every step. Null space approaches are extended to nonlinear complementarity problems. Two different solvers are employed for all NCP in an algorithm. 展开更多
关键词 Global convergence nonlinear complementarity problem nonlinear programming null space methods
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A Class of New Large-Update Primal-Dual Interior-Point Algorithms for P*(k) Nonlinear Complementarity Problems
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作者 Hua Ping CHEN Ming Wang ZHANG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2011年第10期1979-1994,共16页
In this paper we propose a class of new large-update primal-dual interior-point algorithms for P.(k) nonlinear complementarity problem (NCP), which are based on a class of kernel functions investigated by Bai et a... In this paper we propose a class of new large-update primal-dual interior-point algorithms for P.(k) nonlinear complementarity problem (NCP), which are based on a class of kernel functions investigated by Bai et al. in their recent work for linear optimization (LO). The arguments for the algorithms are followed as Peng et al.'s for P.(n) complementarity problem based on the self-regular functions [Peng, J., Roos, C., Terlaky, T.: Self-Regularity: A New Paradigm for Primal-Dual Interior- Point Algorithms, Princeton University Press, Princeton, 2002]. It is worth mentioning that since this class of kernel functions includes a class of non-self-regular functions as special case, so our algorithms are different from Peng et al.'s and the corresponding analysis is simpler than theirs. The ultimate goal of the paper is to show that the algorithms based on these functions have favorable polynomial complexity. 展开更多
关键词 Large-update method interior-point algorithm nonlinear complementarity problem non- self-regular function polynomial complexity
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Multisplitting Iteration Schemes for Solving a Class of Nonlinear Complementarity Problems
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作者 Chen-liang Li Jin-ping Zeng 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2007年第1期79-90,共12页
We consider several synchronous and asynchronous multisplitting iteration schemes for solving a class of nonlinear complementarity problems with the system matrix being an H-matrix. We establish the convergence theore... We consider several synchronous and asynchronous multisplitting iteration schemes for solving a class of nonlinear complementarity problems with the system matrix being an H-matrix. We establish the convergence theorems for the schemes. The numerical experiments show that the schemes are efficient for solving the class of nonlinear complementarity problems. 展开更多
关键词 nonlinear complementarity problems asynchronous iteration H-MATRIX multisplitting method
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RESTRICTED ADDITIVE SCHWARZ METHOD FOR A KIND OF NONLINEAR COMPLEMENTARITY PROBLEM
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作者 Hongru Xu Kekun Huang +1 位作者 Shuilian Xie Zhe Sun 《Journal of Computational Mathematics》 SCIE CSCD 2014年第5期547-559,共13页
In this paper, a new Schwarz method called restricted additive Schwarz method (RAS) is presented and analyzed for a kind of nonlinear complementarity problem (NCP). The method is proved to be convergent by using w... In this paper, a new Schwarz method called restricted additive Schwarz method (RAS) is presented and analyzed for a kind of nonlinear complementarity problem (NCP). The method is proved to be convergent by using weighted maximum norm. Besides, the effect of overlap on RAS is also considered. Some preliminary numerical results are reported to compare the performance of RAS and other known methods for NCP. 展开更多
关键词 nonlinear complementarity problem nonlinear source term Restricted addi-tive Schwarz method Weighted max norm.
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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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PREDICTOR-CORRECTOR METHOD FOR NONLINEAR COMPLEMENTARITY PROBLEM
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作者 罗智泉 吴士泉 叶荫宇 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 1997年第3期321-328,共6页
Recently, Ye et al.[2] proved that the predictor-corrector method proposed by Mizuno et al[1] maintains O( L)-iteration complexity while exhibiting the quadratic convergence of the dual gap to zero under very mild con... Recently, Ye et al.[2] proved that the predictor-corrector method proposed by Mizuno et al[1] maintains O( L)-iteration complexity while exhibiting the quadratic convergence of the dual gap to zero under very mild conditions. This impressive result becomes the best-known in the interior point methods. In this paper, we modify the predictor-corrector method and then extend it to solving the nonlinear complementarity problem. We prove that the new method has a ( log(1/ε))-iteration complexity while maintaining the quadratic asymptotic convergence. 展开更多
关键词 Interior point method nonlinear complementarity problem monotone mapping complexity quadratic convergence
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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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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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