On implicit function theorem for locally Lipschitz equations

• 成果类型: Article
• 署名作者: Arutyunov, Aram, V; Zhukovskiy, Sergey E.
• 署名单位: V.A. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-021-01750-y
• 发表日期: 2023
• 页码: 1107-1120
• 关键词: Optimization

摘要

Equations defined by locally Lipschitz continuous mappings with a parameter are considered. Implicit function theorems for this equation are obtained. The regularity condition is formulated in the terms of the Clarke Jacobian. Implicit functions estimates are derived. It is shown that the considered regularity assumptions are weaker than most of the known ones. The obtained implicit function theorems are applied to derive conditions for upper semicontinuity of the optimal value function for parameterized optimization problems