Lipschitzian multifunctions and a Lipschtzian inverse mapping theorem

• 成果类型: Article
• 署名作者: Levy, AB
• 署名单位: Bowdoin College
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.26.1.105.10600
• 发表日期: 2001
• 页码: 105-118
• 关键词: generalized equations

摘要

We introduce a new class of multifunctions whose graphs under certain kernel inverting matrices, are locally equal to the graphs of Lipschitzian (single-valued) mappings. We characterize the existence of Lipschitzian localizations of these multifunctions in terms of a natural condition on a generalized Jacobian mapping. One corollary to our main result is a Lipschitzian inverse map ping theorem for the broad class of max hypomonotone multifunctions. We apply our theoretical results to the sensitivity analysis of solution mappings associated with parameterized optimization problems. In particular, we obtain new characterizations of the Lipschitzian stability of stationary points and Karush-Kuhn-Tucker pairs associated with parameterized nonlinear programs.