Speaker
Jun Moon (Assistant professor, School of Electrical and Computer Engineering, University of Seoul)
Time & Location
Jul. 25 (Thur) 14:00 / Building 133 Room 316-1
Abstract
In this talk, we study two existence theorems in optimization and their applications to stochastic optimal control and zero-sum differential games. First, we study the Ekeland’s variational principle, which shows the existence of nearly optimal solutions for general optimization problems. As for applications, we consider the stochastic optimal control problem for forward-backward stochastic differential equations, where the Ekeland’s principle is used to establish the necessary condition for optimality. Second, we study the Stegall’s variational principle, which shows the existence of optimal solutions for the linearly perturbed convex functional. Then we consider zero-sum differential games, where the Stegall’s principle is applied to prove uniqueness of the viscosity solution to the HJI equation. As time permits, we study the geometric version of the Hahn-Banach theorem, which asserts that there exists a separating hyperplane between two disjoint convex sets.
Biography
Jun Moon received the B.S. degree in electrical and computer engineering, and the M.S. degree in electrical engineering from Hanyang University, Seoul, South Korea, in 2006 and 2008, respectively. He received the Ph.D. degree in electrical and computer engineering from University of Illinois at Urbana and Champaign, USA, in 2015. From 2008 to 2011, he was a researcher at Agency for Defense Development (ADD) in South Korea. From Feb. 2016 to Feb. 2019, he was an assistant professor at the School of Electrical and Computer Engineering, Ulsan National Institute of Science and Technology (UNIST), South Korea. Since March 2019, he is an assistant professor at the School of Electrical and Computer Engineering, University of Seoul, South Korea. He is a recipient of the Fulbright Graduate Study Award 2011. His research interests include stochastic optimal control, differential games and estimation, distributed optimal control, and mean field games.
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