Structural and stability properties of P0 nonlinear complementarity problems

• 成果类型: Article
• 署名作者: Facchinei, F
• 署名单位: Sapienza University Rome
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.23.3.735
• 发表日期: 1998
• 页码: 735-745
• 关键词: mountain pass theorem; Variational Inequality; set

摘要

We consider P-0 nonlinear complementarity problems and study the connectedness and stability of the solutions by applying degree theory and the Mountain Pass Theorem to a smooth reformulation of the complementarity problem. We show that the solution set is connected and bounded if a bounded isolated component of the solution set exists and that a solution is locally unique if and only if it is globally unique. Furthermore, we prove that a solution is stable in Ha's sense if and only if it is globally unique, while the complementarity problem is stable if and only if the solution set is bounded.