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Average cost Markov control processes with weighted norms: existence of canonical policies

Evgueni Gordienko, Onésimo Hernández-Lerma (1995)

Applicationes Mathematicae

This paper considers discrete-time Markov control processes on Borel spaces, with possibly unbounded costs, and the long run average cost (AC) criterion. Under appropriate hypotheses on weighted norms for the cost function and the transition law, the existence of solutions to the average cost optimality inequality and the average cost optimality equation are shown, which in turn yield the existence of AC-optimal and AC-canonical policies respectively.

Average cost Markov control processes with weighted norms: value iteration

Evgueni Gordienko, Onésimo Hernández-Lerma (1995)

Applicationes Mathematicae

This paper shows the convergence of the value iteration (or successive approximations) algorithm for average cost (AC) Markov control processes on Borel spaces, with possibly unbounded cost, under appropriate hypotheses on weighted norms for the cost function and the transition law. It is also shown that the aforementioned convergence implies strong forms of AC-optimality and the existence of forecast horizons.

Averaging approach to distributed convex optimization for continuous-time multi-agent systems

Wei Ni, Xiaoli Wang (2016)

Kybernetika

Recently, distributed convex optimization has received much attention by many researchers. Current research on this problem mainly focuses on fixed network topologies, without enough attention to switching ones. This paper specially establishes a new technique called averaging-base approach to design a continuous-time distributed algorithm for convex optimization problem under switching topology. This idea of using averaging was proposed in our earlier works for the consensus problem of multi-agent...

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