Second-order characterizations of tilt stability with applications to nonlinear programming

The paper is devoted to the study of tilt-stable local minimizers of general optimization problems in finite-dimensional spaces and its applications to classical nonlinear programs with twice continuously differentiable data. The importance of tilt stability has been well recognized from both theoretical and numerical aspects of optimization, and this notion has been extensively studied in the literature. Based on advanced tools of second-order variational analysis and generalized differentiation, we develop a new approach to tilt stability, which allows us to derive not only qualitative but also quantitative characterizations of tilt-stable minimizers with calculating the corresponding moduli. The implementation of this approach and general results in the classical framework of nonlinear programming provides complete characterizations of tilt-stable minimizers under new second-order qualification and optimality conditions.