Sensitivity Analysis of a Stationary Point Set Map under Total Perturbations. Part 1: Lipschitzian Stability

By applying some theorems of Levy and Mordukhovich (Math Program 99: 311--327, 2004) and other related results, we estimate the Fr\'echet 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).