数学与统计学院学术报告[2021] 118号

(高水平大学建设系列报618号)

报告题目: On solving a class of fractional semi-infinite polynomial programming problems

报告人：郭峰　 副教授  （大连理工大学）

报告时间：2021年11月24日 　14:00-14:50

直播平台及链接： 腾讯会议 会议ID：647 171 244 　 　

报告内容：In this talk, we study a class of fractional semi-infinite polynomial programming (FSIPP) problems, in which the objective is a fraction of a convex polynomial and a concave polynomial, and the constraints consist of infinitely many convex polynomial inequalities. To solve such a problem, we first present a framework to reformulate it to a pair of conic optimization problem and its Lagrangian dual, which reduce to semidefinite programming (SDP) problems if we can bring sum-of-squares structures into the conic constraints. To this end, we provide a characteristic cone constraint qualification for convex semi-infinite programming problems to guarantee strong duality and also the attainment of the solution in the dual problem, which is of its own interest.  In this framework, we first present a hierarchy of SDP relaxations with asymptotic convergence for the FSIPP problem whose index set is defined by finitely many polynomial inequalities.  Next, we study four cases of the FSIPP problems which can be reduced to either a single SDP problem or a finite sequence of SDP problems, where at least one minimizer can be extracted.

报告人简历：

郭峰，大连理工大学数学科学学院副教授，2007年于山东大学获学士学位，2012年于中国科学院数学与系统科学研究院获博士学位。主要从事凸代数几何相关理论研究，包括多项式及半代数优化、半定规划等。

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                                                2021年11月22日