scholarly journals A Kind of Stochastic Eigenvalue Complementarity Problems

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Ying-xiao Wang ◽  
Shou-qiang Du
Keyword(s):  
Complementarity Problem ◽  
Eigenvalue Problems ◽  
Complementarity Problems ◽  
Smoothing Newton Method ◽  
Convergence Properties ◽  
Eigenvalue Complementarity Problem ◽  
Interest In Research ◽  
Global And Local ◽  
The Given ◽  
Nonnegative Constraints

With the development of computer science, computational electromagnetics have also been widely used. Electromagnetic phenomena are closely related to eigenvalue problems. On the other hand, in order to solve the uncertainty of input data, the stochastic eigenvalue complementarity problem, which is a general formulation for the eigenvalue complementarity problem, has aroused interest in research. So, in this paper, we propose a new kind of stochastic eigenvalue complementarity problem. We reformulate the given stochastic eigenvalue complementarity problem as a system of nonsmooth equations with nonnegative constraints. Then, a projected smoothing Newton method is presented to solve it. The global and local convergence properties of the given method for solving the proposed stochastic eigenvalue complementarity problem are also given. Finally, the related numerical results show that the proposed method is efficient.

scholarly journals A new smoothing method for solving nonlinear complementarity problems

2019 ◽  
Vol 17 (1) ◽  
pp. 104-119 ◽  
Author(s):  
Jianguang Zhu ◽  
Binbin Hao
Keyword(s):  
Newton Method ◽  
Quadratic Convergence ◽  
Complementarity Problems ◽  
Nonlinear Complementarity Problem ◽  
Smoothing Newton Method ◽  
Convergence Properties ◽  
Linear System Of Equations ◽  
Complementarity Conditions ◽  
Nonlinear Complementarity ◽  
Global And Local

Abstract In this paper, a new improved smoothing Newton algorithm for the nonlinear complementarity problem was proposed. This method has two-fold advantages. First, compared with the classical smoothing Newton method, our proposed method needn’t nonsingular of the smoothing approximation function; second, the method also inherits the advantage of the classical smoothing Newton method, it only needs to solve one linear system of equations at each iteration. Without the need of strict complementarity conditions and the assumption of P0 property, we get the global and local quadratic convergence properties of the proposed method. Numerical experiments show that the efficiency of the proposed method.

scholarly journals Further Application ofH-Differentiability to Generalized Complementarity Problems Based on Generalized Fisher-Burmeister Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Wei-Zhe Gu ◽  
Mohamed A. Tawhid
Keyword(s):  
Stationary Point ◽  
Complementarity Problem ◽  
Global Minimum ◽  
Complementarity Problems ◽  
Merit Function ◽  
Merit Functions ◽  
Generalized Complementarity Problem ◽  
Nonlinear Complementarity ◽  
Generalized Complementarity Problems ◽  
The Given

We study nonsmooth generalized complementarity problems based on the generalized Fisher-Burmeister function and its generalizations, denoted by GCP(f,g) wherefandgareH-differentiable. We describeH-differentials of some GCP functions based on the generalized Fisher-Burmeister function and its generalizations, and their merit functions. Under appropriate conditions on theH-differentials offandg, we show that a local/global minimum of a merit function (or a “stationary point” of a merit function) is coincident with the solution of the given generalized complementarity problem. When specializing GCP(f,g)to the nonlinear complementarity problems, our results not only give new results but also extend/unify various similar results proved forC1, semismooth, and locally Lipschitzian.

scholarly journals A Smoothing Method with Appropriate Parameter Control Based on Fischer-Burmeister Function for Second-Order Cone Complementarity Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-16 ◽  
Author(s):  
Yasushi Narushima ◽  
Hideho Ogasawara ◽  
Shunsuke Hayashi
Keyword(s):  
Complementarity Problem ◽  
Quadratic Convergence ◽  
Complementarity Problems ◽  
Optimization Problems ◽  
Second Order ◽  
Smoothing Newton Method ◽  
System Of Equations ◽  
Important Class ◽  
Nonsmooth System ◽  
Second Order Cone

We deal with complementarity problems over second-order cones. The complementarity problem is an important class of problems in the real world and involves many optimization problems. The complementarity problem can be reformulated as a nonsmooth system of equations. Based on the smoothed Fischer-Burmeister function, we construct a smoothing Newton method for solving such a nonsmooth system. The proposed method controls a smoothing parameter appropriately. We show the global and quadratic convergence of the method. Finally, some numerical results are given.

scholarly journals A Smoothing Newton Method with a Mixed Line Search for Monotone Weighted Complementarity Problems

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Xiaoqin Jiang ◽  
He Huang
Keyword(s):  
Newton Method ◽  
Complementarity Problem ◽  
Line Search ◽  
Complementarity Problems ◽  
Linear Equations ◽  
Step Length ◽  
Smoothing Newton Method ◽  
System Of Linear Equations ◽  
Weak Assumption ◽  
Mixed Line

In this paper, we present a smoothing Newton method for solving the monotone weighted complementarity problem (WCP). In each iteration of our method, the iterative direction is achieved by solving a system of linear equations and the iterative step length is achieved by adopting a line search. A feature of the line search criteria used in this paper is that monotone and nonmonotone line search are mixed used. The proposed method is new even when the WCP reduces to the standard complementarity problem. Particularly, the proposed method is proved to possess the global convergence under a weak assumption. The preliminary experimental results show the effectiveness and robustness of the proposed method for solving the concerned WCP.

A Smoothing Newton Method for Nonlinear Complementarity Problems

2013 ◽  
Vol 475-476 ◽  
pp. 1090-1093
Author(s):  
Ning Feng ◽  
Zhi Yuan Tian ◽  
Xin Lei Qu
Keyword(s):  
Global Convergence ◽  
Numerical Experiment ◽  
Newton Method ◽  
Complementarity Problem ◽  
Complementarity Problems ◽  
Nonlinear Complementarity Problem ◽  
Nonlinear Complementarity Problems ◽  
Smoothing Newton Method ◽  
Nonlinear Complementarity ◽  
Mild Conditions

A new FB-function based on the P0 function is given in this paper. The nonlinear complementarity problem is reformulated to solve equivalent equations based on the FB-function. A modified smooth Newton method is proposed for nonlinear complementarity problem. Under mild conditions, the global convergence of the algorithm is proved. The numerical experiment shows that the algorithm is potentially efficient.

scholarly journals Numerical Results for the General Linear Complementarity Problem

2019 ◽  
Vol 11 (1) ◽  
pp. 43-46
Author(s):  
Zsolt Darvay ◽  
Ágnes Füstös
Keyword(s):  
Programming Language ◽  
Linear Complementarity Problem ◽  
Interior Point ◽  
Complementarity Problem ◽  
Complementarity Problems ◽  
Linear Complementarity ◽  
Numerical Results ◽  
Interior Point Algorithm ◽  
C Programming Language ◽  
C Programming

Abstract In this article we discuss the interior-point algorithm for the general complementarity problems (LCP) introduced by Tibor Illés, Marianna Nagy and Tamás Terlaky. Moreover, we present a various set of numerical results with the help of a code implemented in the C++ programming language. These results support the efficiency of the algorithm for both monotone and sufficient LCPs.

scholarly journals Generalized AOR Method for Solving Absolute Complementarity Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Muhammad Aslam Noor ◽  
Javed Iqbal ◽  
Khalida Inayat Noor ◽  
E. Al-Said
Keyword(s):  
Complementarity Problem ◽  
Complementarity Problems ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Equivalent Formulation ◽  
Existence Of A Solution ◽  
Absolute Value ◽  
New Class ◽  
Aor Method ◽  
The Absolute

We introduce and consider a new class of complementarity problems, which is called the absolute value complementarity problem. We establish the equivalence between the absolute complementarity problems and the fixed point problem using the projection operator. This alternative equivalent formulation is used to discuss the existence of a solution of the absolute value complementarity problem. A generalized AOR method is suggested and analyzed for solving the absolute the complementarity problems. We discuss the convergence of generalized AOR method for theL-matrix. Several examples are given to illustrate the implementation and efficiency of the method. Results are very encouraging and may stimulate further research in this direction.

scholarly journals Parametric Extended General Mixed Variational Inequalities

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
Muhammad Aslam Noor
Keyword(s):  
Variational Inequalities ◽  
Complementarity Problems ◽  
Equivalent Formulation ◽  
Resolvent Equations ◽  
Special Cases ◽  
General Variational Inequalities ◽  
Significant Extension ◽  
Mixed Variational Inequalities ◽  
The Given

It is well known that the resolvent equations are equivalent to the extended general mixed variational inequalities. We use this alternative equivalent formulation to study the sensitivity of the extended general mixed variational inequalities without assuming the differentiability of the given data. Since the extended general mixed variational inequalities include extended general variational inequalities, quasi (mixed) variational inequalities and complementarity problems as special cases, results obtained in this paper continue to hold for these problems. In fact, our results can be considered as a significant extension of previously known results.

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