Numerical methods and algorithms for solving stochastic dynamic decision problems
| Programmee: | International Collaboration |
| Code: | 13.820.18.01/GA |
| Execution period: | 2013 – 2015 |
| Institutions: | Institute of Mathematics and Computer Science, University of the German Federal Armed Forces (Munich) |
| Project Leader: | Lozovanu Dmitrii |
| Participants: | Kolesnik Alexander, Naval Elvira, Lazari Alexandru, Capcelea Maria |
Summary
The investigations of the project are concerned with elaboration of numerical methods and algorithms for solving a class of stochastic dynamic programming problems that extends classical discrete control problems and Markov decision processes with average and expected total discounted optimization criteria. New algorithms based on dynamic programming and dual linear programming for stochastic versions of discrete optimal control problems and Markov decision processes with finite and infinite time horizon will be proposed and grounded. Additionally the game theoretical approach to these problems will be applied and new class of stochastic positional games that extends deterministic ones will be formulated and studied. Nash equilibria conditions and algorithms for determining the optimal strategies of the players in the considered stochastic games will be derived. The main theoretical investigations of the project are concerned with existence of the solutions for considered problems and correctness of the proposed algorithms. The elaborated algorithms will be implemented in the corresponding software environment and will be placed on webpage.
