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报告题目：Sums of squares, moment matrices and optimization over polynomials系列报告

报告人：郭峰（大连理工大学）

报告时间：2022年8月16日 13:30~14:30 / 17日 08:30~09:30 / 18日 08:30~09:30 / 19日 09:30~10:30

报告地点：腾讯会议  会议号：554 976 5868

报告内容简介：Polynomial optimization refers to minimizing a polynomial function over a set defined by polynomial equations and inequalities, which is NP-hard in general. In the past 20 years, the semidefinite programming (SDP) relaxation methods for polynomial optimization, which can globally solve the problems, have been well studied in the literature. The methodology is based on sums of squares representations of positive polynomials and their dual moment theory. In this lecture, we will introduce in detail this dual pair of theories and their applications in deriving SDP relaxations for polynomial optimization. We will also talk about the applications of the homogenization technique in polynomial optimization related problems with unbounded feasible set. The extensions of the SDP relaxation methods to convex semi-infinite polynomial programming will also be addressed.

报告人简介：郭峰，大连理工大学数学科学学院副教授，硕士生导师。2007年毕业于山东大学，同年保送到中国科学院数学与系统科学研究院，并于2012年获博士学位。主要从事凸代数几何及优化相关理论研究，包括多项式及半代数优化、半定规划、符号数值混合计算、数学机械化等，在SIAM Journal on Optimization, Journal of Global Optimization, Computational Optimization and Applications, ISSAC等国际杂志和国际会议发表及接收发表论文10余篇。主持/参与多项国家自然科学基金项目。

邀请人：矫立国 (助理研究员  jiaolg356@nenu.edu.cn)