报告时间：2021年5月28日， 13:00 - 14:00

报告地点：腾讯会议：ID：287 509 114  PW: 123456

报告人：郭峰 副教授（大连理工大学）

报告摘要：We consider the semi-infinite system of polynomial inequalities of the form K:={x \in R^m | p(x,y)>=0 for all y\in S\subset R^n}, where p(x, y) is a real polynomial in the variables x and the parameters y, the index set S is a basic semialgebraic set in R^n, −p(x, y) is convex in x for every y in S. We propose a procedure to construct approximate semidefinite representations of K. There are two indices to index these approximate semidefinite representations. As two indices increase, these semidefinite representation sets expand and contract, respectively, and can approximate K as closely as possible under some assumptions. In some special cases, we can fix one of the two indices or both. Then, we consider the optimization problem of minimizing a convex polynomial over K. We present an SDP relaxation method for this optimization problem by similar strategies used in constructing approximate semidefinite representations of K. Under certain assumptions, some approximate minimizers of the optimization problem can also be obtained from the SDP relaxations. In some special cases, we show that the SDP relaxation for the optimization problem is exact and all minimizers can be extracted.

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