The 40th Anniversary Celebration of Shenzhen University and the 40th Anniversary Celebration of Mathematics

Liyuan Distinguished Scholar Issue twenty-one

Title:Optimality Conditions and Numerical Algorithms for Constrained Minimax Optimization Problems

Speaker:Mr. Dai Yuhong (Institute of Mathematics and System Sciences, Chinese Academy of Sciences)

Lecture time: December 13, 2023 (Wednesday) 10:10-11:10

Venue: Conference Room 303, Alumni Square, Alumni Plaza, SZU

Overview：It is well known that there have been many numerical algorithms for solving nonsmooth minimax problems, numerical algorithms for nonsmooth minimax problems with joint constraints are very rare. Minimax problems with joint constraints are very rare. This paper aims to discuss optimality conditions and develop practical numerical algorithms for two calsses of minimax problems, i.e., minimax problems with joint constraints and minimax problems with least constraint violation. First of all, we use the properties of proximal mapping and KKT system to establish optimality conditions and develop a proximal gradient multi-step ascent decent First of all, we use the properties of proximal mapping and KKT system to establish optimality conditions and develop a proximal gradient multi-step ascent decent method (PGmsAD) as a numerical algorithm. Furthermore, we demonstrate that the method can establish the same iterative complexity as unconstrained Secondly, we introduce the definition of the local minimax point and investigate the solvability of the dual of the optimization problem with the least constraint violation. Secondly, we introduce the definition of the local minimax point and investigate the solvability of the dual of the optimization problem with the least constraint violation. Moreover, we establish the optimality conditions and propose the augmented Lagrangian method for the convex minimax optimization with the least constraint violation, which has the linear convergence rate under an error bound condition.

Speaker Introduction:Prof. Dai Yuhong, Ph.D. Supervisor,Vice President of the Institute of Mathematics and Systems Research,Chinese Academy of Sciences,President of the Chinese Society of Operations Research and President of the Asia-Pacific Federation of Operational Research Societies (AFORS). Professor Dai has long been engaged in theoretical and applied research on optimization methods, and has made systematic and creative work in continuous optimization, integer programming and applied optimization. He has presided over or is presiding over a number of projects, including the National Outstanding Young Scientist Fund, the Innovative Research Group Project of the National Foundation of China, and the National Key Research and Development Program of the 14th Five-Year Plan. He was invited to give a 45-minute presentation at the International Congress of Mathematicians2022and a one-hour presentation at the24thInternational Congress on Mathematical Planning. He was awarded the Second Prize of National Natural Science, China Youth Science and Technology Award, Zhong Jiaqing Mathematics Prize, Feng Kang Scientific Computing Prize, Chen Shengshen Mathematics Prize, and the First Xiaoshutie Applied Mathematics Prize.

Students and faculty are welcome to attend!

Invited by: School of Mathematical Sciences

School of Mathematical Sciences

December 11, 2023