The Scalarization Approach to Multiobjective Markov Control Problems: Why Does It Work?

Journal Article · Fri Oct 15 00:00:00 EDT 2004 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S00245-004-0804-4· OSTI ID:21067450

Hernandez-Lerma, Onesimo ^[1]; Romera, Rosario ^[2]

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1. Departamento de Matematicas, CINVESTAV-IPN, A. Postal 14-740, Mexico D.F. 07000 (Mexico)
2. Departamento de Mathematicas, Universidad Carlos III of Madrid, Calle Madrid 126, 28903 Getafe, Madrid (Spain)

This paper concerns discrete-time multiobjective Markov control processes on Borel spaces and unbounded costs. Under mild assumptions, it is shown that the usual 'scalarization approach' to obtain Pareto policies for the multiobjective control problem is in fact equivalent to solving the dual of a certain multiobjective infinite-dimensional linear program. The latter program is obtained from a multiobjective measure problem which is also used to prove the existence of strong Pareto policies, that is, Paretopolicies whose cost vector is the closest to the control problem's virtual minimum.

• OSTI ID: 21067450
• Journal Information: Applied Mathematics and Optimization, Vol. 50, Issue 3; Other Information: DOI: 10.1007/s00245-004-0804-4; Copyright (c) 2004 Springer; www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CONTROL THEORY
MARKOV PROCESS
MATHEMATICAL SPACE
VECTORS