On Two Interior-Point Mappings for Nonlinear Semidefinite Complementarity Problems

Authors:
R. D. C. Monteiro;Jong-Shi Pang
Affiliations:
-;-
Venue:
Mathematics of Operations Research
Year:
1998

Citing 0
Cited 3

Semismooth homeomorphisms and strong stability of semidefinite and Lorentz complementarity problems

Mathematics of Operations Research
Limiting behavior of the Alizadeh-Haeberly-Overton weighted paths in semidefinite programming

Optimization Methods & Software
Superlinear Convergence of an Infeasible Predictor-Corrector Path-Following Interior Point Algorithm for a Semidefinite Linear Complementarity Problem Using the Helmberg-Kojima-Monteiro Direction

SIAM Journal on Optimization

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Abstract

Extending our previous work ( Monteiro and Pang 1996), 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. 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 (1996) and Shida, Shindoh, and Kojima (1995), our approach is based on the theory of local homeomorphic maps in nonlinear analysis.