Subregular recourse in nonlinear multistage stochastic optimization

• 成果类型: Article
• 署名作者: Dentcheva, Darinka; Ruszczynski, Andrzej
• 署名单位: Stevens Institute of Technology; Rutgers University System; Rutgers University New Brunswick
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-020-01612-z
• 发表日期: 2021
• 页码: 249-270
• 关键词: l-p; Duality; THEOREM

摘要

We consider nonlinear multistage stochastic optimization problems in the spaces of integrable functions. We allow for nonlinear dynamics and general objective functionals, including dynamic risk measures. We study causal operators describing the dynamics of the system and derive the Clarke subdifferential for a penalty function involving such operators. Then we introduce the concept of subregular recourse in nonlinear multistage stochastic optimization and establish subregularity of the resulting systems in two formulations: with built-in nonanticipativity and with explicit nonanticipativity constraints. Finally, we derive optimality conditions for both formulations and study their relations.