A Note on Linear Complementarity via Two-Person Zero-Sum Games

Abstract

The matrix [Formula: see text] of a linear complementarity problem can be viewed as a payoff matrix of a two-person zero-sum game. Lemke’s algorithm can be successfully applied to reach a complementary solution or infeasibility when the game satisfies the following conditions: (i) Value of [Formula: see text] is equal to zero. (ii) For all principal minors of [Formula: see text] (transpose of [Formula: see text]) value is non-negative. (iii) For any optimal mixed strategy [Formula: see text] of the maximizer either [Formula: see text] or [Formula: see text] for each coordinate [Formula: see text].