Sensitivity analysis of optimization problems under second order regular constraints

J. Frédéric Bonnans, Roberto Cominetti, Alexander Shapiro

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37 Scopus citations

Abstract

We present a perturbation theory for finite dimensional optimization problems subject to abstract constraints satisfying a second order regularity condition. This is a technical condition that is always satisfied in the case of semi-definite optimization. We derive Lipschitz and Holder expansions of approximate optimal solutions, under a directional constraint qualification hypothesis and various second order sufficient conditions that take into account the curvature of the set defining the constraints of the problem. We show how the theory applies to semi-infinite programs in which the contact set is a smooth manifold and the quadratic growth condition in the constraint space holds, and discuss the differentiability of metric projections as well as the Moreau-Yosida regularization. Finally we show how the theory applies to semi-definite optimization.

Original languageEnglish
Pages (from-to)806-831
Number of pages26
JournalMathematics of Operations Research
Volume23
Issue number4
DOIs
StatePublished - 1998

Keywords

  • Directional constraint qualification
  • Directional differentiability
  • Metric projection
  • Optimal value function
  • Parametric optimization
  • Second order optimally conditions
  • Semi-definite programming
  • Semi-infinite programming
  • Sensitivity analysis

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