Abstract
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 we give interconnections between both concepts and extend some ideas to standard nonlinear programs withC 1 data (underC 1 perturbations). The main purpose of this paper is to survey several equivalent characterizations of strong stability in the classical case of programs withC 2 data underC 2 perturbations. The unified approach proposed here is essentially based on arguments from the analysis of Lipschitzian mappings.
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Sponsored by the International Institute for Applied Systems Analysis (IIASA), Laxenburg, Austria.
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Klatte, D., Tammer, K. Strong stability of stationary solutions and Karush-Kuhn-Tucker points in nonlinear optimization. Ann Oper Res 27, 285–307 (1990). https://doi.org/10.1007/BF02055199
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DOI: https://doi.org/10.1007/BF02055199