Academic Report
Title: Multi-objective optimization problems with SOS-convex polynomials over an LMI constraint
Reporter: Doc. JIAO Liguo (Suzhou University)
Time: June 1, 2019 (Monday) PM 16:00-17:00
Location: A1101# room, Innovation Park Building
Contact: A. Prof. GUO Feng (tel:84708351-8088)
Abstract: Consider Multi-objective optimization problems (MP) with SOS-convex polynomials over an LMI constraint. In this talk, we aim to find efficient solutions of the problem (MP). We do this by using two scalarization approaches, that is, the -constraint method and the hybrid method. More precisely, we first transform the problem (MP) into its scalar forms by the \epsilon-constraint method and the hybrid method, respectively. Then, strong duality results, between each formulated scalar problem and its associated semidefinite programming dual problem, are given, respectively. Moreover, we show that the optimal solution to the proposed (two) scalar problems can be found by solving its associated single semidefinite programming problem, under some suitable regularity conditions. As a consequence, we prove that finding efficient solutions to the problem (MP) can be done by employing the two scalarization approaches. Besides, some nontrivial numerical examples are also given to show how to find efficient solutions to the problem (MP).
The brief introduction to the reporter: Dr. Jiao Liguo received his Ph.D. degree in Applied Mathematics from Puqing University in Korea in 2018. He is currently working as a postdoctoral fellow at the School of Mathematics, Suzhou University. His main research areas are multi-objective programming and robust optimization. He has made many significant contributions to the optimization conditions and the existence of solutions of related optimization problems. At present, more than 10 papers have been published in authoritative international magazines.
