This talk consists of two parts. In the first part, we survey results for general optimal control problems with state constraints via dynamic programming approach. Due to the constraints, the value function could be discontinuous and viscosity solution characterization of HJB equation for the value function becomes difficult. In the second part, we report some recent results on optimal impulse problems with terminal state constraints.
Jiongmin Yong is a professor of mathematics at University of Central Florida. He obtain his BS degree in 1982 at Fudan University, and his PhD degree in 1986 at Purdue University, under supervision of L. D. Berkovitz. Professor Yong’s research interests include control theory, stochastic differential/integral equations, and mathematical finance. He was teaching in Fudan University during 1988—2003, promoted to a full professor in 1991, and became a Cheung Kong Professor in 2000. He was the chair of Department of Mathematics at Fudan University during 2000—2003. Since 2003, he has been a professor at University of Central Florida. Professor Yong was/is an associate editor of several journals, including SIAM Journal on Control and Optimization, ESAIM: Control, Optimization and Calculus of Variations, and Mathematical Control and Related Topics. He won a number of honors, including Su Buqing Mathematical Prize, SAIG/SCT Best SICON Paper Prize, and was invited to deliver a 45-minute talk at 2014 ICM.