There exit several high speed computation applications that requires minimum distance computation between nodes in weighted graph. Dedicated techniques exist for this purpose are called as shortest path computation. Depending upon need of application, there are three type of shortest path problems; Single Source Shortest Path (SSSP), Single Destination Shortest Path (SDSP) and All Pair Shortest...

This work treats Hamilton-Jacobi-Bellman equations. Their relation to several problems in mathematics is presented and an introduction to viscosity solutions is given. The work of several research articles is reviewed, including the Barles-Souganidis convergence argument and the inaugural papers on mean-field games. Original research on numerical methods for Hamilton-Jacobi-Bellman equations is...

Introduction In the theory of dynamic programming (Bellman, 1957; Bellman and Dreyfus, 1962), the Bellman principle of optimality was not called into question until Rudd and Blum found a wrong solution for a chemical reaction system (Jackson, 1963; Rudd and Blum, 1962). Although the Bellman principle of optimality is true for almost all practical problems, there are still some problems, both th...

This paper investigates possible methods of parallelizing two common single source path-finding algorithms. This research could enable faster computation of optimal path planning in complex environments. Both algorithms, A* and Bellman-Ford were found to be parallelizable. After testing, A* was shown to lack good scaling potential while Bellman-Ford showed promise as a scalable parallel path fi...

Several recent papers have proposed recursive Lagrangian-basedmethods for solving dynamic contracting problems. Thesemethods give rise to Bellman operators that incorporate either a dual inf-sup or a saddle point operation. We give conditions that ensure the Bellman operator implied by a dual recursive formulation is contractive. JEL codes: C61, C73, D82, E61.

We consider approximation methods for Markov decision processes in the learning and simulation context. For policy evaluation based on solving approximate versions of a Bellman equation, we propose the use of weighted Bellman mappings. Such mappings comprise weighted sums of one-step and multistep Bellman mappings, where the weights depend on both the step and the state. For projected versions ...

We study existence and uniqueness of a fixed point for the Bellman operator in deterministic dynamic programming. Without any topological assumption, we show that the Bellman operator has a unique fixed point in a restricted domain, that this fixed point is the value function, and that the value function can be computed by value iteration.