The convergence of the multiplicative multisplitting-type method for solving the linear complementarity problem with an H-matrix is discussed using classical and new results from the theory of splitting. This directly results in a sufficient condition for guaranteeing the convergence of the multiplicative multisplitting method. Moreover, the multiplicative multisplitting method is applied to th...

We consider a modiication of a path-following infeasible-interior-point algorithm described by Wright. In the new algorithm, we attempt to improve each major iterate by reusing the coeecient matrix factors from the latest step. We show that the modiied algorithm has similar theoretical global convergence properties to those of the earlier algorithm, while its asymptotic convergence rate can be ...

In this paper, we first present a brief infeasible interior-point method with full-Newton step for solving linear complementarity problem (LCP). The main iteration consists of a feasibility step and several centrality steps. First we present a full Newton step infeasible interior-point algorithm based on the classic logarithmical barrier function. After that a specific kernel function is introd...

First we give a short description of the Extended Linear Complementarity Problem (ELCP), which is a mathematical programming problem. We brieey discuss how this problem can be used in the analysis of discrete event systems and continuous variable systems. Next we show that the ELCP can also be used to model and to analyze hybrid systems. More speciically, we consider a traac-light-controlled in...

The max-plus algebra is one of the frameworks that can be used to model discrete event systems. We show that many fundamental problems in the maxplus algebra can be reformulated as a mathematical programming problem: the Extended Linear Complementarity Problem.

*Correspondence: [email protected] School of Mathematics and Information Science, Baoji University of Arts and Sciences, Baoji, P.R. China Abstract An alternative error bound for linear complementarity problems for BS-matrices is presented. It is shown by numerical examples that the new bound is better than that provided by García-Esnaola and Peña (Appl. Math. Lett. 25(10):1379–1383, 2012) i...

Based on a well-known reformulation of the linear complementarity problem (LCP) as a nondifferentiable system of nonlinear equations, a Newton-type method will be described for the solution of LCPs. Under certain assumptions, it will be shown that this method has a finite termination property, i.e., if an iterate is sufficiently close to a solution of LCP, the method finds this solution in one ...

In this paper we propose a class of new large-update primal-dual interior-point algorithms for P∗(κ) 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∗(κ) complementarity problem based on the self-regular functio...