| Article ID: | iaor20162399 |
| Volume: | 169 |
| Issue: | 3 |
| Start Page Number: | 902 |
| End Page Number: | 924 |
| Publication Date: | Jun 2016 |
| Journal: | Journal of Optimization Theory and Applications |
| Authors: | Laurire Mathieu, Pironneau Olivier |
| Keywords: | optimization, simulation, allocation: resources, combinatorial optimization, stochastic processes |
We investigate a model problem for optimal resource management. The problem is a stochastic control problem of mean‐field type. We compare a Hamilton–Jacobi–Bellman fixed‐point algorithm to a steepest descent method issued from calculus of variations. For mean‐field type control problems, stochastic dynamic programming requires adaptation. The problem is reformulated as a distributed control problem by using the Fokker–Planck equation for the probability distribution of the stochastic process; then, an extended Bellman’s principle is derived by a different argument than the one used by P. L. Lions. Both algorithms are compared numerically.