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Robust shortest path planning and semicontractive dynamic programming

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  • Dimitri P. Bertsekas

Abstract

In this article, we consider shortest path problems in a directed graph where the transitions between nodes are subject to uncertainty. We use a minimax formulation, where the objective is to guarantee that a special destination state is reached with a minimum cost path under the worst possible instance of the uncertainty. Problems of this type arise, among others, in planning and pursuit‐evasion contexts, and in model predictive control. Our analysis makes use of the recently developed theory of abstract semicontractive dynamic programming models. We investigate questions of existence and uniqueness of solution of the optimality equation, existence of optimal paths, and the validity of various algorithms patterned after the classical methods of value and policy iteration, as well as a Dijkstra‐like algorithm for problems with nonnegative arc lengths.© 2016 Wiley Periodicals, Inc. Naval Research Logistics 66:15–37, 2019

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  • Dimitri P. Bertsekas, 2019. "Robust shortest path planning and semicontractive dynamic programming," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(1), pages 15-37, February.
    • Handle: RePEc:wly:navres:v:66:y:2019:i:1:p:15-37
    DOI: 10.1002/nav.21697
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    1. L. Grüne & O. Junge, 2008. "Global Optimal Control of Perturbed Systems," Journal of Optimization Theory and Applications, Springer, vol. 136(3), pages 411-429, March.
    2. Dimitri P. Bertsekas & John N. Tsitsiklis, 1991. "An Analysis of Stochastic Shortest Path Problems," Mathematics of Operations Research, INFORMS, vol. 16(3), pages 580-595, August.
    3. Dimitri P. Bertsekas & Huizhen Yu, 2012. "Q-Learning and Enhanced Policy Iteration in Discounted Dynamic Programming," Mathematics of Operations Research, INFORMS, vol. 37(1), pages 66-94, February.
    4. Huizhen Yu & Dimitri Bertsekas, 2013. "Q-learning and policy iteration algorithms for stochastic shortest path problems," Annals of Operations Research, Springer, vol. 208(1), pages 95-132, September.
    5. Stuart E. Dreyfus, 1969. "An Appraisal of Some Shortest-Path Algorithms," Operations Research, INFORMS, vol. 17(3), pages 395-412, June.
    6. Alexander Vladimirsky, 2008. "Label-Setting Methods for Multimode Stochastic Shortest Path Problems on Graphs," Mathematics of Operations Research, INFORMS, vol. 33(4), pages 821-838, November.
    7. Blai Bonet, 2007. "On the Speed of Convergence of Value Iteration on Stochastic Shortest-Path Problems," Mathematics of Operations Research, INFORMS, vol. 32(2), pages 365-373, May.
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