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 Implementation of an Interior-point Algorithm for Linear Complementarity Problem Working in a Wide Neighborhood

2019 ◽  
Vol 11 (1) ◽  
pp. 47-50
Author(s):  
Zsolt Darvay ◽  
Attila-Szabolcs Orbán
Keyword(s):  
Linear Complementarity Problem ◽  
Interior Point ◽  
Complementarity Problem ◽  
Linear Complementarity Problems ◽  
Linear Complementarity ◽  
Point Of View ◽  
Interior Point Algorithm ◽  
C Programming Language ◽  
C Programming ◽  
Theoretical Results

Abstract In this article, we study the interior-point algorithm for solving linear complementarity problems, published by Xiaouje Ma, Hongwei Liu, Jianke Zhang and Weijie Cong from the implementation point of view. The algorithm was implemented in C++ programming language, thus supporting the effectiveness of the method. Despite the fact that the theoretical results refer only to the monotone linear complementarity problem, practical testing showed that the algorithm also works well in more general cases.

scholarly journals Long step homogeneous interior point algorithm for the p* nonlinear complementarity problems

2002 ◽  
Vol 12 (1) ◽  
pp. 17-48
Author(s):  
Goran Lesaja
Keyword(s):  
Global Convergence ◽  
Linear Complementarity Problem ◽  
Interior Point ◽  
Complementarity Problem ◽  
Complementarity Problems ◽  
Nonlinear Complementarity Problem ◽  
Linear Complementarity ◽  
Compact Set ◽  
Interior Point Algorithm ◽  
Nonlinear Complementarity

A P*-Nonlinear Complementarity Problem as a generalization of the P*-Linear Complementarity Problem is considered. We show that the long-step version of the homogeneous self-dual interior-point algorithm could be used to solve such a problem. The algorithm achieves linear global convergence and quadratic local convergence under the following assumptions: the function satisfies a modified scaled Lipschitz condition, the problem has a strictly complementary solution, and certain submatrix of the Jacobian is nonsingular on some compact set.

A primal-dual interior-point method based on a new kernel function for linear complementarity problem

2019 ◽  
Vol 12 (07) ◽  
pp. 2050001
Author(s):  
El Amir Djeffal ◽  
Mounia Laouar
Keyword(s):  
Linear Complementarity Problem ◽  
Interior Point ◽  
Complementarity Problem ◽  
Small Neighborhood ◽  
Linear Complementarity ◽  
Central Path ◽  
Search Direction ◽  
Interior Point Algorithm ◽  
Newton Step ◽  
Primal Dual

In this paper, we present an interior-point algorithm for solving an optimization problem using the central path method. By an equivalent reformulation of the central path, we obtain a new search direction which targets at a small neighborhood of the central path. For a full-Newton step interior-point algorithm based on this search direction, the complexity bound of the algorithm is the best known for linear complementarity problem. For its numerical tests, some strategies are used and indicate that the algorithm is efficient.

A New Searching Direction for Linear Complementarity Problems

2011 ◽  
Vol 219-220 ◽  
pp. 1089-1092
Author(s):  
Li Pu Zhang ◽  
Ying Hong Xu
Keyword(s):  
Linear Complementarity Problem ◽  
Complementarity Problem ◽  
Quadratic Convergence ◽  
Complementarity Problems ◽  
Convergence Property ◽  
Linear Complementarity Problems ◽  
Linear Complementarity ◽  
Simple Function ◽  
Interior Point Algorithm ◽  
Local Quadratic Convergence

In this paper, we investigate the properties of a simple function. As an application, we present a full-step interior-point algorithm for linear complementarity problem. The algorithm uses the simple function to determine the searching direction and define the neighborhood of central path. The full-step used in the algorithm has local quadratic convergence property according to the proximity function which is also constructed by this simple function. We derive the iteration complexity for the algorithm and obtain the best-known iteration bounds for linear complementarity problem.

Solving Obstacle Problem Based on Potential-Reduction Interior Point Algorithm

2010 ◽  
Vol 29-32 ◽  
pp. 725-731
Author(s):  
Long Quan Yong
Keyword(s):  
Linear Complementarity Problem ◽  
Interior Point ◽  
Complementarity Problem ◽  
Obstacle Problem ◽  
Linear Complementarity Problems ◽  
Linear Complementarity ◽  
Interior Point Algorithm ◽  
Potential Reduction ◽  
Standard Linear ◽  
Novel Method

This text studies a kind of obstacle problem. Combining with difference principle, we transform the original problem into monotone linear complementarity problem, and propose a novel method called potential-reduction interior point algorithm for monotone linear complementarity problem. We establish global and finite convergence of the new method. The reliability and efficiency of the algorithm is demonstrated by the numerical experiments of standard linear complementarity problems and the examples of obstacle problem with free boundary.

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