报告主题：Local versus global conditions in polynomial optimization
报告人：聂家旺 教授（加州大学圣地亚哥分校）
报告时间：2016年9月20日（周二）14:00
报告地点：校本部G507
邀请人：白延琴 教授
主办部门：永利数学系
报告摘要：This talk compares local and global conditions for polynomial optimization problems. First, we review the classical local optimality conditions: constraint qualification, strict complementarity and second order sufficiency conditions. We show that they are always satisfied, except a zero measure set of input data. Second, we review global optimality conditions that are expressed by sum-of-squares type representations. We show that if the above classical local optimality conditions hold, then the sum-of-squares type global optimality conditions must be satisfied. Third, we review Lasserre's hierarchy for solving polynomial optimization, and show that it always has finite convergence, except a zero measure set of input data.
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