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

摘要

The matrix M 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 M is equal to zero. (ii) For all principal minors of MT (transpose of M) value is non-negative. (iii) For any optimal mixed strategy y of the maximizer either yi>0 or (My)i>0 for each coordinate i.