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The average cost optimality equation: a fixed point approach. (English) Zbl 1176.90626
Summary: We are concerned with the expected average cost optimal control problem for discrete-time Markov control processes with Borel spaces and possibly unbounded costs. We show, under a Lyapunov stability condition and a growth condition on the costs, the existence of an stationary optimal policy using a well-known fixed point theorem.

MSC:
90C40 Markov and semi-Markov decision processes
93E20 Optimal stochastic control
49J55 Existence of optimal solutions to problems involving randomness
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