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.
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