On Two Interior-Point Mappings for Nonlinear Semidefinite Complementarity Problems

Renato D.C.Monteiro and Jong-Shi Pang

Extending our previous work \cite{monpang-2}, this paper studies properties of two fundamental mappings associated with the family of interior-point methods for solving monotone nonlinear complementarity problems over the cone of symmetric positive semidefinite matrices. The first of these maps lead to a family of new continuous trajectories which include the central trajectory as a special case. The trajectories of this family completely ``fill up'' the set of interior feasible points of the problem in the same way as the weighted central paths ``fill up'' the interior feasible region of a linear program. Unlike the approach based on the theory of maximal monotone maps taken by Shida, Shindoh \cite{shida-shindoh} and Shida, Shindoh, and Kojima \cite{shida-shindoh-kojima-1}, our approach is based on the theory of local homeomorphic maps in nonlinear analysis.

Contact: monteiro@isye.gatech.edu