Conditions for the Solvability of the Linear Programming Formulation for Constrained Discounted Markov Decision Processes

Journal Article · Mon Aug 15 00:00:00 EDT 2016 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S00245-015-9307-3· OSTI ID:22617268

Dufour, F., E-mail: [e-mail] ^[1]; Prieto-Rumeau, T., E-mail: [e-mail] ^[2]

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1. Institut de Mathématiques de Bordeaux, INRIA Bordeaux Sud Ouest, Team: CQFD, and IMB (France)
2. UNED, Department of Statistics and Operations Research (Spain)

We consider a discrete-time constrained discounted Markov decision process (MDP) with Borel state and action spaces, compact action sets, and lower semi-continuous cost functions. We introduce a set of hypotheses related to a positive weight function which allow us to consider cost functions that might not be bounded below by a constant, and which imply the solvability of the linear programming formulation of the constrained MDP. In particular, we establish the existence of a constrained optimal stationary policy. Our results are illustrated with an application to a fishery management problem.

• OSTI ID: 22617268
• Journal Information: Applied Mathematics and Optimization, Vol. 74, Issue 1; Other Information: Copyright (c) 2016 Springer Science+Business Media New York; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
COMPACTS
FUNCTIONS
HYPOTHESIS
LINEAR PROGRAMMING
MANAGEMENT
MARKOV PROCESS