报告题目:On Genericity and Holder Stability Results for Semi-algebraic Variational Inequality Problems

报告人：Gue Myung Lee 教授

报告时间：15:30-16:30

报告地点： 仁和107

题目：On Genericity and Holder Stability Results for Semi-algebraic Variational Inequality Problems 时间地点：1月11日(周五) 15:30-16:30 仁和107 报告人：Gue Myung Lee 教授(Pukyong National University, Korea) 摘要：The variational inequality problem provides a general framework for the study of optimization and equilibrium problems. The attention of this talk is paid to the genericity and H"older stability in semi-algebraic variational inequality problems, covering, in particular, affine variational inequality problems and necessary optimization conditions for polynomial optimization problems. We first show that semi-algebraic variational inequality problems have  generically finitely many solutions, around each of which they admit a unique set of active constraint indices and such solutions are non-degenerate.  Then we characterize various types of globally upper Holder continuity of the solution map of the parameterized variational inequality problem. We also establish a bounded Holder stability property for the solution map of the problem.  Finally, we show that if the solution map is lower semi-continuous at a reference point then the corresponding solution set is finite. This investigation is a continuation of our recent works on genericity and stability properties for semi-algebraic optimization problems (Gue Myung Lee and  Tien Son Pham: Journal of Optimization Theory and Applications 2016,  Gue Myung Lee and Tien Son Pham: SIAM Journal on Optimization 2017). This talk is based upon the paper written by Jae Hyoung Lee, Pham Tien Son  and Gue Myung Lee and published in Journal of Optimization Theory and Applications on 2018.