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

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• 作者：B. S. Mordukhovich (1)
  T. T. A. Nghia (1)
  
  1. Department of Mathematics ; Wayne State University ; Detroit ; MI ; 48202 ; USA
  
• 关键词：49J53 ; 90C31 ; 90C99
• 刊名：Mathematical Programming
• 出版年：2015
• 出版时间：February 2015
• 年：2015
• 卷：149
• 期：1-2
• 页码：83-104
• 全文大小：275 KB
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  13. Mordukhovich, B.S.: Variational Analysis and Generalized Differentiation, I: Basic Theory, II: Applications. Springer, Berlin (2006)
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• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Calculus of Variations and Optimal Control
  Mathematics of Computing
  Numerical Analysis
  Combinatorics
  Mathematical and Computational Physics
  Mathematical Methods in Physics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1436-4646

文摘

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.