On Genericity and Holder Stability Results for Semi-algebraic Variational Inequality Problems
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Title: On Genericity and Holder StabilityResults for Semi-algebraic Variational Inequality Problems
Speaker: Gue Myung Lee (Pukyong NationalUniversity)
Time: 16:00-17:00, January 9, 2019
Location: Room 200-9, 2th Floor, Sir ShawRun Run Business Administration building, School of Mathematical Sciences,Yuquan Campus
Abstract: The variational inequalityproblem provides a general framework for the study of optimization andequilibrium problems. The attention of this talk is paid to the genericity andHolder stability in semi-algebraic variational inequality problems, covering,in particular, affine variational inequality problems and necessaryoptimization conditions for polynomial optimization problems. We first showthat semi-algebraic variational inequality problems have generically finitelymany solutions, around each of which they admit a unique set of activeconstraint indices and such solutions are non-degenerate. Then we characterizevarious types of globally upper Holder continuity of the solution map of theparameterized variational inequality problem. We also establish a boundedHolder stability property for the solution map of the problem. Finally, we showthat if the solution map is lower semi-continuous at a reference point then thecorresponding solution set is finite. This investigation is a continuation ofour recent works on genericity and stability properties for semi-algebraicoptimization problems (Gue Myung Lee and Tien Son Pham: Journal of OptimizationTheory and Applications 2016, Gue Myung Lee and Tien Son Pham: SIAM Journal onOptimization 2017).
Contact person: Chong Li (cli@zju.edu.cn)