Subregular recourse in nonlinear multistage stochastic optimization

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