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General Interior-Point Maps and Existence of Weighted
Paths for Nonlinear Semidefinite Complementarity Problems

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Renato Monteiro and Paulo Zanjacomo

Extending the previous work of Monteiro and Pang (1996b), this paper
studies properties of fundamental maps that can be used to describe
the central path of the monotone nonlinear complementarity problems
over the cone of symmetric positive semidefinite matrices. Instead of
focusing our attention on a specific map as was done in the approach
of Monteiro and Pang (1996b), this paper considers a general form of a
fundamental map and introduces conditions on the map that allow us to
extend the main results of Monteiro and Pang (1996b) to this general
map. Each fundamental map leads to a family of ``weighted''
continuous trajectories which include the central trajectory as a
special case. Hence, for complementarity problems over the cone of
symmetric positive semidefinite matrices, the notion of weighted
central path depends on the fundamental map used to represent the
central path.

Contact: paulo@isye.gatech.edu