Stochastic Optimal Control and Linear Programming Approach

被引：32
|
作者：
Buckdahn, R. [2 ]
Goreac, D. [1 ]
Quincampoix, M. [2 ]
机构：
[1] Univ Paris Est Marne la Vallee, Lab Anal & Math Appl, UMR 8050, F-77454 Marne La Vallee 2, France
[2] Univ Bretagne Occidentale, Unite CNRS 6205, Math Lab, F-29200 Brest, France
来源：
APPLIED MATHEMATICS AND OPTIMIZATION | 2011年 / 63卷 / 02期
关键词：
Linear programming; Stochastic control under constraints; Occupational measures; Viscosity solutions; Long-time averaging; RUN AVERAGE PROBLEMS; OCCUPATION MEASURES; EXISTENCE;
D O I：
10.1007/s00245-010-9120-y
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study a classical stochastic optimal control problem with constraints and discounted payoff in an infinite horizon setting. The main result of the present paper lies in the fact that this optimal control problem is shown to have the same value as a linear optimization problem stated on some appropriate space of probability measures. This enables one to derive a dual formulation that appears to be strongly connected to the notion of (viscosity sub) solution to a suitable Hamilton-Jacobi-Bellman equation. We also discuss relation with long-time average problems.
引用
收藏
页码：257 / 276
页数：20
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