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Optimization in infinite time horizon
- Speaker(s)
- Kamila Łyczek (doktorantka MIM)
- Affiliation
- Uniwersytet Warszawski
- Date
- Nov. 30, 2016, 2:15 p.m.
- Room
- room 4050
- Seminar
- Seminar of Biomathematics and Game Theory Group
Pontryagin's maximum principle is used in optimal control theory to find
the best possible control for taking a dynamical system from one state
to another, especially in the presence of constraints for the state or
input controls. It has as a special case the Euler–Lagrange equation of
the calculus of variations.
Maximum principle cannot be used for infinite-horizon optimal control problems, which appear for example in many fields of economics. Typically, the initial state is fixed and the terminal state (at infinity) is free in such problems, while the utility functional to be maximized is given by an improper integral on the time interval. S. M. Aseev and V. M. Veliov have formulated a proper version of the Pontryagin's maximum principle for the infinite-horizon problem.
I will talk what could happend when we use normal form of maximum principle for infinite time, about results of Aseev and Velov, and about a plan how to expand this optimization for dynamical games.
Maximum principle cannot be used for infinite-horizon optimal control problems, which appear for example in many fields of economics. Typically, the initial state is fixed and the terminal state (at infinity) is free in such problems, while the utility functional to be maximized is given by an improper integral on the time interval. S. M. Aseev and V. M. Veliov have formulated a proper version of the Pontryagin's maximum principle for the infinite-horizon problem.
I will talk what could happend when we use normal form of maximum principle for infinite time, about results of Aseev and Velov, and about a plan how to expand this optimization for dynamical games.
