Title: On Genericity and Holder Stability Results for Semi-algebraic Variational Inequality Problems

Speaker: Gue Myung Lee (Pukyong National University)

Time: 16:00-17:00, January 9, 2019

Location: Room 200-9, 2th Floor, Sir Shaw Run Run Business Administration building, School of Mathematical Sciences, Yuquan Campus

Abstract: 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 Holder 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).

Contact person: Chong Li (cli@zju.edu.cn)