Topic：Local versus global conditions in polynomial optimization
Speaker：Prof. Jiawang Nie (The University California, San Diego)
Abstarct: 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.