Second-order Characterizations of Tilt Stability with Applications to Nonlinear Programming

Boris Mordukhovich (borismath.wayne.edu)
Nghia Tran (nghiamath.wayne.edu)

Abstract: 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.

Keywords: Variational analysis and optimization, first-order and second-order generalized differentiation, Lipschitzian stability, second-order growth, tilt stability

Category 1: Convex and Nonsmooth Optimization

Category 2: Nonlinear Optimization

Citation: Math. Program. Ser A

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Entry Submitted: 07/16/2013
Entry Accepted: 07/16/2013
Entry Last Modified: 11/30/2013

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