Strong stability of stationary solutions and Karush-Kuhn-Tucker points in nonlinear optimization

The concepts of strongly stable stationary solutions (in Kojima’s sense) and of strongly regular Karush-Kuhn-Tucker points (in Robinson’s sense) for optimization problems with twice differentiable data are crucial in theory and applications of nonlinear optimization with data perturbations. In this paper the authors give interconnections between both concepts and extend some ideas to standard nonlinear programs with C¹ data (under C¹ perturbations). The main purpose of this paper is to survey several equivalent characterizations of strong stability in the classical case of programs with C² data under C² perturbations. The unified approach proposed here is essentially based on arguments from the analysis of Lipschitzian mappings.