Label-Setting Methods for Multimode Stochastic Shortest Path Problems on Graphs

• 成果类型: Article
• 署名作者: Vladimirsky, Alexander
• 署名单位: Cornell University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.1080.0321
• 发表日期: 2008
• 页码: 821-838
• 关键词: hamilton-jacobi equations; ordered upwind methods; level set method; Efficient algorithms; implementation

摘要

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).