New extremal principles with applications to stochastic and semi-infinite programming

• 成果类型: Article
• 署名作者: Mordukhovich, Boris S.; Perez-Aros, Pedro
• 署名单位: Wayne State University; Universidad de O'Higgins
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-020-01548-4
• 发表日期: 2021
• 页码: 527-553
• 关键词: variational analysis; linear regularity; infinite; nonsmooth; optimization; calculus; supremum; systems; sets

摘要

This paper develops new extremal principles of variational analysis that are motivated by applications to constrained problems of stochastic programming and semi-infinite programming without smoothness and/or convexity assumptions. These extremal principles concern measurable set-valued mappings/multifunctions with values in finite-dimensional spaces and are established in both approximate and exact forms. The obtained principles are instrumental to derive via variational approaches integral representations and upper estimates of regular and limiting normals cones to essential intersections of sets defined by measurable multifunctions, which are in turn crucial for novel applications to stochastic and semi-infinite programming.