A Newton-type algorithm for generalized linear complementarity problem over a polyhedral cone

A new type of solution method for the generalized linear complementarity problem over a polyhedral cone

“…The global convergence and R-linear con- vergence under mild conditions are established. The conditions guaranteeing the global convergence in this paper are weaker than those in the existing resolving methods in [1,4,5], since the assumption on the existence of a nondegenerate solution is removed. Numerical experiments show that the method has good stability and a promising numerical performance.…”

“…The GLCP is a special case of the generalized nonlinear complementarity problem concerned with how to find the applications in economics, operations research, nonlinear analysis, etc. [1−3] Some issues on numerical resolving methods and solution existence for the problem have been discussed in the literature (e. g., [1,4,5]), and most of these resolving methods are based on the optimization reformulation of the problem. We will present a new type of method for solving the GLCP based on the global error bound estimation in this paper.…”

The Solution Structure and Error Estimation for The Generalized Linear Complementarity Problem

“…The generalized linear complementarity problem, abbreviated as GLCP, is to find vector * n xR  such that * * 0 * * ( ) , ( ) , ( ) ( ) 0, The GLCP is a direct generalization of the classical linear complementarity problem (LCP) and a special case of the general variational inequalities problem(GVI)( [1]). The GLCP was deeply discussed [1,2,3,4] after the work in [5]. The GLCP plays a significant role in economics, engineering, supply chain network equilibrium, etc.…”

“…Up to now, the issues of solution structure and numerical solution methods for GLCP were fully discussed in the literature (e.g., [2,3,4,5,10,11,12]). To our knowledge, Mangasarian and Shiau ( [13]) are the first one who gave the solution structure and error estimation analysis to LCP.…”

Algorithm design for a supply chain equilibrium management model

“…Many researchers, especially scholars abroad, are increasingly interested, and great progress has been made in both theoretical research and practical applications. To solve (1), many algorithms have been proposed ( [4,5,6,7,9]). The basic idea of these algorithms is to transform (1) into an unconstrained optimization problem, or into a simple constrained optimization problem ( [4,7,9]), and then to use the Newton type algorithms or confidence region algorithms.…”