Semismooth homeomorphisms and strong stability of semidefinite and Lorentz complementarity problems

J.-S. Pang, Defeng Sun, J. Sun

Research output: Journal article publicationJournal articleAcademic researchpeer-review

93 Citations (Scopus)

Abstract

Based on an inverse function theorem for a system of semismooth equations, this paper establishes several necessary and sufficient conditions for an isolated solution of a complementarity problem defined on the cone of symmetric positive semidefinite matrices to be strongly regular/stable. We show further that for a parametric complementarity problem of this kind, if a solution corresponding to a base parameter is strongly stable, then a semismooth implicit solution function exists whose directional derivatives can be computed by solving certain affine problems on the critical cone at the base solution. Similar results are also derived for a complementarity problem defined on the Lorentz cone. The analysis relies on some new properties of the directional derivatives of the projector onto the semidefinite cone and the Lorentz cone.
Original languageEnglish
Pages (from-to)39-63
Number of pages25
JournalMathematics of Operations Research
Volume28
Issue number1
DOIs
Publication statusPublished - 1 Jan 2003
Externally publishedYes

Keywords

  • Complementarity problem
  • Lorentz cone
  • Semidefinite cone
  • Variational inequality

ASJC Scopus subject areas

  • Mathematics(all)
  • Computer Science Applications
  • Management Science and Operations Research

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