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Title: Stochastic Optimal Control and Linear Programming Approach

Abstract

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.

Authors:
 [1];  [2];  [1]
  1. Universite de Bretagne Occidentale, Laboratoire de Mathematiques, unite CNRS 6205 (France)
  2. Laboratoire d'Analyse et de Mathematiques Appliquees, Universite Paris-Est Marne-la-Vallee (France)
Publication Date:
OSTI Identifier:
22043932
Resource Type:
Journal Article
Journal Name:
Applied Mathematics and Optimization
Additional Journal Information:
Journal Volume: 63; Journal Issue: 2; Other Information: Copyright (c) 2011 Springer Science+Business Media, LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0095-4616
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; HAMILTON-JACOBI EQUATIONS; LINEAR PROGRAMMING; MATHEMATICAL SOLUTIONS; OPTIMAL CONTROL; OPTIMIZATION; PROBABILITY; SPACE; STOCHASTIC PROCESSES

Citation Formats

Buckdahn, R, Goreac, D, and Quincampoix, M. Stochastic Optimal Control and Linear Programming Approach. United States: N. p., 2011. Web. doi:10.1007/S00245-010-9120-Y.
Buckdahn, R, Goreac, D, & Quincampoix, M. Stochastic Optimal Control and Linear Programming Approach. United States. https://doi.org/10.1007/S00245-010-9120-Y
Buckdahn, R, Goreac, D, and Quincampoix, M. 2011. "Stochastic Optimal Control and Linear Programming Approach". United States. https://doi.org/10.1007/S00245-010-9120-Y.
@article{osti_22043932,
title = {Stochastic Optimal Control and Linear Programming Approach},
author = {Buckdahn, R and Goreac, D and Quincampoix, M},
abstractNote = {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.},
doi = {10.1007/S00245-010-9120-Y},
url = {https://www.osti.gov/biblio/22043932}, journal = {Applied Mathematics and Optimization},
issn = {0095-4616},
number = 2,
volume = 63,
place = {United States},
year = {Fri Apr 15 00:00:00 EDT 2011},
month = {Fri Apr 15 00:00:00 EDT 2011}
}