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

## Abstract

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.

- Authors:

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

- Publication Date:

- OSTI Identifier:
- 22617268

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Applied Mathematics and Optimization; Journal Volume: 74; Journal 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)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; COMPACTS; FUNCTIONS; HYPOTHESIS; LINEAR PROGRAMMING; MANAGEMENT; MARKOV PROCESS

### Citation Formats

```
Dufour, F., E-mail: dufour@math.u-bordeaux1.fr, and Prieto-Rumeau, T., E-mail: tprieto@ccia.uned.es.
```*Conditions for the Solvability of the Linear Programming Formulation for Constrained Discounted Markov Decision Processes*. United States: N. p., 2016.
Web. doi:10.1007/S00245-015-9307-3.

```
Dufour, F., E-mail: dufour@math.u-bordeaux1.fr, & Prieto-Rumeau, T., E-mail: tprieto@ccia.uned.es.
```*Conditions for the Solvability of the Linear Programming Formulation for Constrained Discounted Markov Decision Processes*. United States. doi:10.1007/S00245-015-9307-3.

```
Dufour, F., E-mail: dufour@math.u-bordeaux1.fr, and Prieto-Rumeau, T., E-mail: tprieto@ccia.uned.es. Mon .
"Conditions for the Solvability of the Linear Programming Formulation for Constrained Discounted Markov Decision Processes". United States.
doi:10.1007/S00245-015-9307-3.
```

```
@article{osti_22617268,
```

title = {Conditions for the Solvability of the Linear Programming Formulation for Constrained Discounted Markov Decision Processes},

author = {Dufour, F., E-mail: dufour@math.u-bordeaux1.fr and Prieto-Rumeau, T., E-mail: tprieto@ccia.uned.es},

abstractNote = {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.},

doi = {10.1007/S00245-015-9307-3},

journal = {Applied Mathematics and Optimization},

number = 1,

volume = 74,

place = {United States},

year = {Mon Aug 15 00:00:00 EDT 2016},

month = {Mon Aug 15 00:00:00 EDT 2016}

}

Other availability

Save to My Library

You must Sign In or Create an Account in order to save documents to your library.