Displaying similar documents to “Dynamic programming in constrained Markov decision processes”

Sample path average optimality of Markov control processes with strictly unbounded cost

Oscar Vega-Amaya (1999)

Applicationes Mathematicae

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We study the existence of sample path average cost (SPAC-) optimal policies for Markov control processes on Borel spaces with strictly unbounded costs, i.e., costs that grow without bound on the complement of compact subsets. Assuming only that the cost function is lower semicontinuous and that the transition law is weakly continuous, we show the existence of a relaxed policy with 'minimal' expected average cost and that the optimal average cost is the limit of discounted programs. Moreover,...

Sample-path average cost optimality for semi-Markov control processes on Borel spaces: unbounded costs and mean holding times

Oscar Vega-Amaya, Fernando Luque-Vásquez (2000)

Applicationes Mathematicae

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We deal with semi-Markov control processes (SMCPs) on Borel spaces with unbounded cost and mean holding time. Under suitable growth conditions on the cost function and the mean holding time, together with stability properties of the embedded Markov chains, we show the equivalence of several average cost criteria as well as the existence of stationary optimal policies with respect to each of these criteria.

The linear programming approach to deterministic optimal control problems

Daniel Hernández-Hernández, Onésimo Hernández-Lerma, Michael Taksar (1996)

Applicationes Mathematicae

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Given a deterministic optimal control problem (OCP) with value function, say J * , we introduce a linear program ( P ) and its dual ( P * ) whose values satisfy sup ( P * ) ≤ inf ( P ) ≤ J * ( t , x ) . Then we give conditions under which (i) there is no duality gap