报告人： Tien-Son PHAM教授  越南大叻大学

报告题目：Local minimizers of semi-algebraic functions

报告时间：2019/7/1(周一)下午3:00-4:00

报告地点：创新园大厦A1101

报告校内联系人：郭 峰 副教授       联系电话：84708351-8088

报告摘要：

Consider a semi-algebraic function f: R^N->R, which is continuous around a point \bar{x}. Using the so-called tangency variety of f at \bar{x}, we first provide necessary and sufficient conditions for \bar{x} to be a local minimizer of f, and then in the case where \bar{x} is an isolated local minimizer of f, we define a ``tangency exponent'' \alpha_*>0 so that for any \alpha the following four conditions are always equivalent:  

1) the inequality \alpha>\alpha_* holds;

2) the point \bar{x} is an \alpha-order sharp local minimizer of f

3) the limiting subdifferential \partial f of f is (\alpha-1)-order strongly metrically subregular at \bar{x} for 0; and

4) the function f satisfies the Lojaseiwcz gradient inequality at \bar{x} with the exponent 1-1/(\alpha).

Besides, we also present a counterexample to a conjecture posed by Drusvyatskiy and Ioffe in [Math. Program. Ser. A, 153(2):635--653, 2015].

报告人简介： Tien-Son PHAM教授的主要研究领域为奇异性理论及多项式优化等方面，在Łojasiewicz不等式，多项式函数广义关键值及多项式优化半定规划松弛等问题中做出了许多重要的工作，在国际权威杂志上发表论文近60篇，出版专著1本，其中在SIAM Journal on Optimization，Mathematical Programming等优秀杂志上发表论文10余篇。

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2019/6/27