Optimality Conditions for Parabolic Stochastic Optimal Control Problems with Boundary Controls

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

Applied Mathematics and Optimization Pub Date : 2024-12-09 DOI:10.1007/s00245-024-10204-8

Piero Visconti

引用次数: 0

Abstract

In this paper, we study optimality conditions for a class of control problems driven by a cylindrical Wiener process, resulting in a stochastic maximum principle in differential form. The control acts on both the drift and volatility, potentially as unbounded operators, allowing for SPDEs with boundary control and/or noise. Through the factorization method, we establish a regularity property for the state equation, which, by duality, extends to the backward costate equation, understood in the transposition sense. Finally, we show that the cost functional is Gâteaux differentiable, with its derivative represented by the costate. The optimality condition is derived using results from set-valued analysis.

查看原文本刊更多论文

具有边界控制的抛物型随机最优控制问题的最优性条件

本文研究了一类由圆柱形Wiener过程驱动的控制问题的最优性条件，得到了微分形式的随机极大值原理。控制作用于漂移和波动，可能作为无界算子，允许具有边界控制和/或噪声的spde。通过因式分解方法，我们建立了状态方程的正则性，并通过对偶性将其推广到转置意义上的后向状态方程。最后，我们证明了代价泛函是g teaux可微的，其导数由代价状态表示。利用集值分析的结果，导出了最优性条件。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Applied Mathematics and Optimization 数学-应用数学

CiteScore

3.30

自引率

5.60%

发文量

103

审稿时长

>12 weeks

期刊介绍： The Applied Mathematics and Optimization Journal covers a broad range of mathematical methods in particular those that bridge with optimization and have some connection with applications. Core topics include calculus of variations, partial differential equations, stochastic control, optimization of deterministic or stochastic systems in discrete or continuous time, homogenization, control theory, mean field games, dynamic games and optimal transport. Algorithmic, data analytic, machine learning and numerical methods which support the modeling and analysis of optimization problems are encouraged. Of great interest are papers which show some novel idea in either the theory or model which include some connection with potential applications in science and engineering.