Monotone Semidefinite Complementarity Problems

Masayuki Shida and Susumu Shindoh

In this paper, we study some basic properties of the monotone semidefinite nonlinear complementarity problem (SDCP). We show that the trajectory continuously accumulates into the solution set of the SDCP passing through the set of the infeasible but positive semidefinite matrices under certain conditions. Especially, for the monotone semidefinite linear complementarity problems, the trajectory converges to an analytic center of the solution set. Finally, we propose the globally convergent infeasible-interior-point algorithm for the SDCP.

Research Reports on Mathematical and Computing Sciences B-312, March 1996.