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

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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.

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Acknowledgments

The authors are grateful to anonymous referees and editors of the paper for their very careful reading and a number of helpful remarks that allowed us to essentially improve the original presentation.

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Authors and Affiliations

  1. Department of Mathematics, Wayne State University, Detroit, MI, 48202, USA

    B. S. Mordukhovich & T. T. A. Nghia

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  1. B. S. Mordukhovich
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  2. T. T. A. Nghia
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Correspondence to B. S. Mordukhovich.

Additional information

This research was supported by the National Science Foundation under grant DMS-1007132.

B. S. Mordukhovich was also partly supported by the Australian Research Council under grant DP-12092508 and by the Portuguese Foundation of Science and Technologies under grant MAT/11109.

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Mordukhovich, B.S., Nghia, T.T.A. Second-order characterizations of tilt stability with applications to nonlinear programming. Math. Program. 149, 83–104 (2015). https://doi.org/10.1007/s10107-013-0739-8

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  • DOI: https://doi.org/10.1007/s10107-013-0739-8

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