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Gue Myung LEE (gmleepknu.ac.kr) Abstract: In this paper we consider the class of polynomial optimization problems with inequality and equality constraints, in which every problem of the class is obtained by perturbations of the objective function, while the constraint functions are kept fixed. Under certain assumptions, we establish some stability properties (e.g., strong H\"older stability with explicitly determined exponents, semicontinuity, etc.) of the global solution map, the KarushKuhnTucker setvalued map, and of the optimal value function for all problems in the class. It is shown that for almost every problem in the class, there is a unique optimal solution for which the global quadratic growth condition and the strong secondorder sufficient conditions hold. Further, under local perturbations to the objective function, the optimal solution and the optimal value function (resp., the KarushKuhnTucker setvalued map) vary smoothly (resp., continuously) and the active constraints are constant. As a nice consequence, for almost all polynomial optimization problems, we can find a natural sequence of computationally feasible semidefinite programs, whose solutions give rise to a sequence of points in $\mathbb{R}^n$ converging to the optimal solution of the original problem. Keywords: Semialgebraic programs, Global solution map, Optimal value function, KarushKuhnTucker setvalued map, Stability, Genericity, Strong secondorder sufficient conditions, Quadratic growth Category 1: Global Optimization Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization ) Citation: Download: [PDF] Entry Submitted: 06/09/2015 Modify/Update this entry  
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