TY - JOUR
T1 - Subregular recourse in nonlinear multistage stochastic optimization
AU - Dentcheva, Darinka
AU - Ruszczyński, Andrzej
N1 - Publisher Copyright:
© 2021, Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society.
PY - 2021/9
Y1 - 2021/9
N2 - 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.
AB - 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.
KW - Nonanticipativity
KW - Nonlinear Causal Operators
KW - Subregularity
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U2 - 10.1007/s10107-020-01612-z
DO - 10.1007/s10107-020-01612-z
M3 - Article
AN - SCOPUS:85099416115
SN - 0025-5610
VL - 189
SP - 249
EP - 270
JO - Mathematical Programming
JF - Mathematical Programming
IS - 1-2
ER -