Some Properties of Solution to Semidefinite Complementarity Problem

Yu Chen,Cuiling Chen,Caihong Han

doi:10.4236/jamp.2018.61012

Abstract

In this paper, we discuss the nonemptyness and boundedness of the solution set for P*-semidefinite complementarity problem by using the concept of exceptional family of elements for complementarity problems over the cone of semidefinite matrices, and obtain a main result that if the corresponding problem has a strict feasible point, then its solution set is nonemptyness and boundedness.

Highlights

IntroductionThis paper deals with semidefinite complementarity problem (SDCP). Let χ denote the space of n × n block-diagonal real matrices with m blocks of sizes ( ) n1, n2 , , nm
We discuss the nonemptyness and boundedness of the solution set for P* -semidefinite complementarity problem by using the concept of exceptional family of elements for complementarity problems over the cone of semidefinite matrices, and obtain a main result that if the corresponding problem has a strict feasible point, its solution set is nonemptyness and boundedness
This paper deals with semidefinite complementarity problem (SDCP)

Summary

Introduction

This paper deals with semidefinite complementarity problem (SDCP). Let χ denote the space of n × n block-diagonal real matrices with m blocks of sizes ( ) n1, n2 , , nm. Isac et al [5] introdued a more general notion of exceptional family of elements Using this notation, some existence theorems of a solution to nonlinear complementarity problems were presented in [5] [6] [7]. In this paper, Motivated by the previous researches, we discuss the nonemptyness and boundedness of the solution set for P* -semidefinite complementarity problem by using the concept of exceptional family of elements for complementarity problems over the cone of semidefinite matrices, and we prove that if the corresponding problem has a strict feasible point, its solution set is nonemptyness and boundedness.

Preliminaries

Main Result

Conclusion