Semismooth homeomorphisms and strong stability of semidefinite and Lorentz complementarity problems

• 成果类型: Article
• 署名作者: Pang, JS; Sun, DF; Sun, J
• 署名单位: Johns Hopkins University; National University of Singapore; National University of Singapore
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.28.1.39.14258
• 发表日期: 2003
• 页码: 39-63
• 关键词: implicit-function theorem; sensitivity-analysis; Newton method; differentiability

摘要

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.