scholarly journals Projective algorithms for solving complementarity problems

2002 ◽  
Vol 29 (2) ◽  
pp. 99-113
Author(s):  
Caroline N. Haddad ◽  
George J. Habetler
Keyword(s):  
Linear Complementarity Problem ◽  
Complementarity Problem ◽  
Convex Sets ◽  
Complementarity Problems ◽  
Linear Complementarity ◽  
Von Neumann ◽  
Nonconvex Sets ◽  
Neumann Type ◽  
Successive Over Relaxation ◽  
Projective Algorithms

We present robust projective algorithms of the von Neumann type for the linear complementarity problem and for the generalized linear complementarity problem. The methods, an extension of Projections Onto Convex Sets (POCS) are applied to a class of problems consisting of finding the intersection of closed nonconvex sets. We give conditions under which convergence occurs (always in2dimensions, and in practice, in higher dimensions) when the matrices areP-matrices (though not necessarily symmetric or positive definite). We provide numerical results with comparisons to Projective Successive Over Relaxation (PSOR).

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 Two-step modulus-based matrix splitting iteration method for horizontal linear complementarity problems

Filomat ◽  
2020 ◽  
Vol 34 (7) ◽  
pp. 2171-2184
Author(s):  
Lu Jia ◽  
Xiang Wang ◽  
Xuan-Sheng Wang
Keyword(s):  
Theoretical Analysis ◽  
Linear Complementarity Problem ◽  
Iteration Method ◽  
Complementarity Problem ◽  
Numerical Experiments ◽  
Complementarity Problems ◽  
Linear Complementarity Problems ◽  
Linear Complementarity ◽  
Matrix Splitting ◽  
Splitting Iteration Method

The modulus-based matrix splitting iteration has received substantial attention as a momentous tool for complementarity problems. For the purpose of solving the horizontal linear complementarity problem, we introduce the two-step modulus-based matrix splitting iteration method. We also show the theoretical analysis of the convergence. Numerical experiments illustrate the effectiveness of the proposed approach.

A globally convergent damped Gauss–Newton method for solving the extended linear complementarity problem

2015 ◽  
Vol 23 (3) ◽  
Author(s):  
Na Huang ◽  
Changfeng Ma
Keyword(s):  
Newton Method ◽  
Linear Complementarity Problem ◽  
Complementarity Problem ◽  
Complementarity Problems ◽  
Optimization Problems ◽  
Linear Complementarity Problems ◽  
Linear Complementarity ◽  
System Of Equations ◽  
Extended Linear Complementarity Problem ◽  
Special Cases

AbstractThe extended linear complementarity problem (denoted by XLCP), of which the linear and horizontal linear complementarity problems are two special cases, can be reformulated as the solution of a nonsmooth system of equations. By the symmetrically perturbed smoothing Fischer-Burmeister function, the XLCP is approximated by a family of parameterized smoothness optimization problems. Asmoothing damped Gauss-Newton method is designed for solving the XLCP. The proposed algorithm is proved to be convergent globally under suitable assumptions. Some numerical results are reported in the paper

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.

scholarly journals The Solution Set Characterization and Error Bound for the Extended Mixed Linear Complementarity Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-15
Author(s):  
Hongchun Sun ◽  
Yiju Wang
Keyword(s):  
Error Bound ◽  
Linear Complementarity Problem ◽  
Complementarity Problem ◽  
Complementarity Problems ◽  
Linear Complementarity Problems ◽  
Linear Complementarity ◽  
Solution Set ◽  
Global Error Bound ◽  
Mixed Linear Complementarity Problem

For the extended mixed linear complementarity problem (EML CP), we first present the characterization of the solution set for the EMLCP. Based on this, its global error bound is also established under milder conditions. The results obtained in this paper can be taken as an extension for the classical linear complementarity problems.

scholarly journals Extensions of P-property, R0-property and semidefinite linear complementarity problems

2017 ◽  
Vol 27 (2) ◽  
pp. 135-151
Author(s):  
I. Jeyaraman ◽  
Kavita Bisht ◽  
K.C. Sivakumar
Keyword(s):  
Linear Transformation ◽  
Linear Complementarity Problem ◽  
Complementarity Problem ◽  
Complementarity Problems ◽  
Linear Complementarity Problems ◽  
Linear Complementarity ◽  
Linear Transformations ◽  
Semidefinite Linear Complementarity Problems ◽  
Semidefinite Linear Complementarity Problem

In this manuscript, we present some new results for the semidefinite linear complementarity problem, in the context of three notions for linear transformations, viz., pseudo w-P property, pseudo Jordan w-P property and pseudo SSM property. Interconnections with the P#-property (proposed recently in the literature) is presented. We also study the R#-property of a linear transformation, extending the rather well known notion of an R0-matrix. In particular, results are presented for the Lyapunov, Stein, and the multiplicative transformations

scholarly journals A Preconditioned Multisplitting and Schwarz Method for Linear Complementarity Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Cuiyu Liu ◽  
Chen-liang Li
Keyword(s):  
Convergence Rate ◽  
Iterative Methods ◽  
Linear Complementarity Problem ◽  
Complementarity Problem ◽  
Numerical Experiments ◽  
Complementarity Problems ◽  
Linear Complementarity Problems ◽  
Linear Complementarity ◽  
Coefficient Matrix ◽  
Schwarz Method

The preconditioner presented by Hadjidimos et al. (2003) can improve on the convergence rate of the classical iterative methods to solve linear systems. In this paper, we extend this preconditioner to solve linear complementarity problems whose coefficient matrix isM-matrix orH-matrix and present a multisplitting and Schwarz method. The convergence theorems are given. The numerical experiments show that the methods are efficient.

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.

SOLVING STRONGLY MONOTONE LINEAR COMPLEMENTARITY PROBLEMS

2013 ◽  
Vol 15 (04) ◽  
pp. 1340035 ◽  
Author(s):  
A. CHANDRASHEKARAN ◽  
T. PARTHASARATHY ◽  
V. VETRIVEL
Keyword(s):  
Linear Complementarity Problem ◽  
Complementarity Problem ◽  
Complementarity Problems ◽  
Linear Complementarity Problems ◽  
Linear Complementarity ◽  
Inner Product ◽  
General Linear ◽  
Strongly Monotone ◽  
Semidefinite Linear Complementarity Problems ◽  
Lipschitz Constants

Given a linear transformation L on a finite dimensional real inner product space V to itself and an element q ∈ V we consider the general linear complementarity problem LCP (L, K, q) on a proper cone K ⊆ V. We observe that the iterates generated by any closed algorithmic map will converge to a solution for LCP (L, K, q), whenever L is strongly monotone. Lipschitz constants of L is vital in establishing the above said convergence. Hence we compute the Lipschitz constants for certain classes of Lyapunov, Stein and double-sided multiplicative transformations in the setting of semidefinite linear complementarity problems. We give a numerical illustration of a closed algorithmic map in the setting of a standard linear complementarity problem. On account of the difficulties in numerically implementing such algorithms for general linear complementarity problems, we give an alternative algorithm for computing the solution for a special class of strongly monotone semidefinite linear complementarity problems along with a numerical example.

Sign in / Sign up

Export Citation Format

Share Document