Subdifferentiation of integral functionals

• 成果类型: Article
• 署名作者: Giner, Emmanuel; Penot, Jean-Paul
• 署名单位: Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Universite Paris Cite; Sorbonne Universite
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-017-1204-x
• 发表日期: 2018
• 页码: 401-431
• 关键词: spaces l-p; limiting subdifferentials; REGULARITY; subgradients; clarke; optimization; Duality

摘要

We examine how the subdifferentials of nonconvex integral functionals can be deduced from the subdifferentials of the corresponding integrand or at least be estimated with the help of them. In fact, assuming some regularity properties of the integrands, we obtain exact expressions for the subdifferentials of the integral functionals. We draw some consequences in terms of duality for such integral functionals, extending in this way the early work of Rockafellar to the nonconvex case.