Subregular recourse in nonlinear multistage stochastic optimization

Darinka Dentcheva, Andrzej Ruszczyński

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)249-270
Number of pages22
JournalMathematical Programming
Volume189
Issue number1-2
DOIs
StatePublished - Sep 2021

All Science Journal Classification (ASJC) codes

  • Software
  • Mathematics(all)

Keywords

  • Nonanticipativity
  • Nonlinear Causal Operators
  • Subregularity

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