Journal
MATHEMATICS OF OPERATIONS RESEARCH
Volume 33, Issue 4, Pages 821-838Publisher
INFORMS
DOI: 10.1287/moor.1080.0321
Keywords
stochastic shortest path; dynamic programming; label-setting; Dijkstra's method; Dial's method; optimal control; Hamilton-Jacobi PDEs; fast marching method
Funding
- National Science Foundation (NSF) [DMS-0514487, CTS-0426787]
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Stochastic shortest path (SSP) problems arise in a variety of discrete stochastic control contexts. An optimal solution to such a problem is typically computed using the value function, which can be found by solving the corresponding dynamic programming equations. In the deterministic case, these equations can be often solved by highly efficient label-setting methods (such as Dijkstra's and Dial's algorithms). In this paper we de. ne and study a class of multimode stochastic shortest path (MSSP) problems and develop sufficient conditions for the applicability of label-setting methods. We illustrate our approach in a number of discrete stochastic control examples. We also discuss the relationship of SSPs with discretizations of static Hamilton-Jacobi equations and provide an alternative derivation for several fast (noniterative) numerical methods for these partial differential equations (PDEs).
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