SEMIDEFINITE PROGRAMMING RELAXATIONS IN MULTI-OBJECTIVE CONVEX POLYNOMIAL OPTIMIZATION

Thời gian: 10:00 đến 11:30 Ngày 20/02/2019

Địa điểm: C2-714, VIASM

Báo cáo viên: JAE HYOUNG LEE (Pukyong National University)

Tóm tắt:

In this talk, we focus on finding efficient solutions for a multi-objective opti-mization problem with convex polynomial data. We first prove an existence result of efficient solutions of the proposed multi-objective optimization problem under some mild assump-tion. By employing hybrid method, we consider a (scalar) convex polynomial optimization problem to find efficient solutions of the proposed multi-objective optimization. We do this by establishing two kind representation of non-negativity of convex polynomials over convex semi-algebraic sets, and then we propose two kind finite convergence results of the Lasserre-type hierarchy of semidefinite programming relaxations for the (scalar) convex polynomial optimization problem under suitable assumptions. As a result, we show that finding efficient solutions of the proposed multi-objective optimization can be done via solving hierarchies of semidefinite programming relaxations and checking a flat truncation condition.

(Liguo Jiao) Finance·Fishery·Manufacture Industrial Mathematics Center on Big Data, Pusan National University, Busan 46241, Korea
Email address: hanchezi@163.com

(Jae Hyoung Lee) Department of Applied Mathematics, Pukyong National University, Bu-san, 48513, Korea
Email address: mc7558@naver.com

(Nithirat Sisarat) Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand
Email address: nithirats@hotmail.com