Iterative Descent Algorithms for a Row Sufficient Linear Complementarity Problem

Abstract

The class of row sufficient linear complementarity problems was introduced in a recent paper by Cottle, Pang, and Venkateswaran [Linear Algebra Appl., 114/115 (1989), pp. 231–249]. In the present paper, two iterative descent algorithms for solving such a linear complementarity problem are developed. One of the algorithms is based on a symmetric variational inequality formulation of the problem, and the other algorithm is an interior-point method which requires a strict feasibility assumption on the problem. Convergence of both algorithms is established. As a by-product of the investigation, a certain property of a column sufficient matrix is uncovered which leads to a constructive way of determining the solvability of a column sufficient linear complementarity problem.