论文标题
非线性多阶段随机优化中的次级求程
Subregular Recourse in Nonlinear Multistage Stochastic Optimization
论文作者
论文摘要
我们考虑在可集成函数空间中的非线性多阶段随机优化问题。我们允许非线性动力学和一般目标功能，包括动态风险度量。我们研究了描述系统动力学的因果运营商，并为涉及此类操作员的惩罚函数提供了Clarke subdfatiential。然后，我们在非线性多阶段随机优化中介绍了亚规定的概念，并以两种公式建立了所得系统的次级性质：具有内置的非预期性和显式的非预期性约束。最后，我们为配方提供了最佳条件并研究其关系。
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.
