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Monotone mappings in dynamic programming

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1 Author(s)
Dimitri P. Bertsekas ; University of Illinois at Urbana-Champaign, Urbana, Illinois

In this paper we consider a class of monotone mappings underlying many sequential optimization problems over a finite or infinite horizon which are of interest in applications. This class of problems Includes deterministic and stochastic optimal control problems, minimax control problems, Semi-Markov Decision problems and others. We prove some fixed point properties of the optimal value function and we analyze the convergence properties of a related generalized Dynamic Programming algorithm. We also give a sufficient condition for convergence, which is widely applicable and considerably strengthens known related results.

Published in:

Decision and Control including the 14th Symposium on Adaptive Processes, 1975 IEEE Conference on

Date of Conference:

10-12 Dec. 1975