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Journal of Optimization Theory and Applications

, Volume 35, Issue 4, pp 581–610 | Cite as

Optimal switching among a finite number of Markov processes

  • B. Doshi
Contributed Papers

Abstract

This paper investigates the problem of the optimal switching among a finite number of Markov processes, generalizing some of the author's earlier results for controlled one-dimensional diffusion. Under rather general conditions, it is shown that the optimal discounted cost function is the unique solution of a functional equation. Under more restrictive assumptions, this function is shown to be the unique solution of some quasi-variational inequalities. These assumptions are verified for a large class of control problems. For controlled Markov chains and controlled one-dimensional diffusion, the existence of a stationary optimal policy is established. Finally, a policy iteration method is developed to calculate an optimal stationary policy, if one exists.

Key Words

Markov decision processes optimal switching discounted costs quasi-variational inequalities stationary optimal policy policy iteration 

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Copyright information

© Plenum Publishing Corporation 1981

Authors and Affiliations

  • B. Doshi
    • 1
  1. 1.Bell LaboratoriesHolmdel

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