The continuity of the solution map in linear complementarity problems with underlyingk-matrices
Huynh The Phung, Tran Thien Tin · Optimization · 2013
By , we denote the solution set of the linear complementarity problem : Find satisfying where is a fixed n-square matrix and is an n-vector. So is a set-valued map from to . In this paper, we will prove that, if is a k-matrix, that is for all , then the solution map of the linear complementarity problem is continuous at every interior point of its domain. The relationship between k-matrices and other matrix classes will also be discussed.