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This paper is devoted to the study of tilt stability of local minimizers forclassical nonlinear programs with equality and inequality constraints in finitedimensions described by twice continuously differentiable functions. Theimportance of tilt stability has been well recognized from both theoretical andnumerical perspectives of optimization, and this area of research has drawnmuch attention in the literature, especially in recent years. Based on advancedtechniques of variational analysis and generalized differentiation, we derivehere complete pointbased second-order characterizations of tilt-stableminimizers entirely in terms of the initial program data under the newqualification conditions, which are the weakest ones for the study of tiltstability.

Complete Characterizations of Tilt Stability in Nonlinear Programming under Weakest Qualification Conditions