Necessary optimality conditions for constrained optimization problems under relaxed constraint qualifications

• 成果类型: Article
• 署名作者: Arutyunov, A. V.; Avakov, E. R.; Izmailov, A. F.
• 署名单位: Lomonosov Moscow State University; Peoples Friendship University of Russia; Russian Academy of Sciences
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-006-0082-4
• 发表日期: 2008
• 页码: 37-68
• 关键词: inequality-type constraints; lipschitzian derivatives; extremum conditions; abnormal problems; local-structure; equality-type; zero-set; mappings; points; ORDER

摘要

We derive first- and second-order necessary optimality conditions for set-constrained optimization problems under the constraint qualification-type conditions significantly weaker than Robinson's constraint qualification. Our development relies on the so-called 2-regularity concept, and unifies and extends the previous studies based on this concept. Specifically, in our setting constraints are given by an inclusion, with an arbitrary closed convex set on the right-hand side. Thus, for the second-order analysis, some curvature characterizations of this set near the reference point must be taken into account.