On two interior-point mappings for nonlinear semidefinite complementarity problems

Extending our previous work, 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 leads to a family of new continuous trajectories which include the central trajectory as a special case. These trajectories completely ‘fill up’ the set of interior feasible points of the problem in the same way as the weighted central paths do the interior of the feasible region of a linear program. Unlike the approach based on the theory of maximal monotone maps taken by Shida and Shindoh, and Shida et al., our approach is based on the theory of local homeomorphic maps in nonlinear analysis.