Sensitivity Analysis of a Stationary Point Set Map Under Total Perturbations. Part 1: Lipschitzian Stability - Huyen, Duong Thi Kim; Yao, Jen-Chih; Yen, Nguyen Dong (Journal of optimization theory and applications, 2019)
By applying some theorems of Levy and Mordukhovich (Math Program 99:311–327, 2004 ) and other related results, we estimate the Fréchet coderivative and the Mordukhovich coderivative of the stationary point set map of a smooth parametric optimization problem with one smooth functional constraint under total perturbations. From the obtained formulas, we derive necessary and sufficient conditions for the local Lipschitz-like property of the stationary point set map. This leads us to new insights into the preceding deep investigations of Levy and Mordukhovich in the above-cited paper and of Qui (J Optim Theory Appl 161:398–429, 2014 , J Glob Optim 65:615–635, 2016 ).