Deterministic and stochastic methods for solving optimization and control problems
| Programmee: | State Programs and Grants |
| Code: | 20.80009.5007.13 |
| Execution period: | 2020 – 2023 |
| Institutions: | Vladimir Andrunachievici Institute of Mathematics and Computer Science |
| Project Leader: | Lozovanu Dmitrii |
| Participants: | Mathematical Modeling |
| Scientific report: | Raport științific 2020 Raport științific 2021 Raport științific 2022 Raport științific 2023 Raport științific final 2020 - 2023 |
Summary
The investigations in the project are concerned with the elaboration and theoretical argumentation of methods and numerical algorithms for solving the optimization and control problems for deterministic and stochastic systems with finite and infinite time horizon. The considered problems comprise the classical discrete optimal control problems, Markov decision problems the variants of multi-criteria and game theory Markov decision processes, diffusion and queuing theory problems and some classes of solid bodies and gas mechanics problems. The main results of the project are related to the following elaborations:
- finding of the optimal stationary and non-stationary strategies for the deterministic and stochastic discrete optimal control problems;
- obtaining the necessary and sufficient conditions for the existence of stationary and non-stationary solutions in the sense of Pareto, Nash and Stackelberg for the multi-criteria and game variants of Markov decision problems with average and total discounted cost optimization criteria;
- finding the stationary and non-stationary Nash equilibrium for stochastic positional games and Shapley stochastic games;
- investigations of finite velocity diffusion processes and finding the characteristic functions for such processes;
- investigations of the problems of solid body and the fluid mechanics to obtain there efficient solutions.
The considered models, methods and algorithms will be used for the analysis of the growth economic models, solving the problems of solid body and gas mechanics, the diffusion problems and queuing theory problems. The expected scientific results will be published and presented at various prestigious scientific forums.
