Centers of Monotone Generalized Complementarity Problems

Masayuki Shida, Susumu Shindoh, and Masakazu Kojima

This paper studies the existence and the continuity of centers of a monotone generalized complementarity problem over $C$ and $\FC$: Find an $(\x,\y) \in \FC \cap (C \times C^*)$ such that $\x\cdot\y = 0$. Here $C^*=\{\y\in\EC : \x \cdot \y \geq 0\ \mbox{ for all }\x\in C\}$ denotes the dual cone of $C$. The main result of the paper unifies and extends some results established for monotone complementarity problems in the Euclidean space and monotone semidefinite linear complementarity problems.

Research Reports on Information Sciences B-303, Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, August 1995.