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Perturbation analysis of second-order cone programming problems

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Abstract

We discuss first and second order optimality conditions for nonlinear second-order cone programming problems, and their relation with semidefinite programming problems. For doing this we extend in an abstract setting the notion of optimal partition. Then we state a characterization of strong regularity in terms of second order optimality conditions. This is the first time such a characterization is given for a nonpolyhedral conic problem.

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Authors and Affiliations

  1. Projet Sydoco, INRIA Rocquencourt, B.P. 105, Le Chesnay, France

    J. Frédéric Bonnans

  2. Department of Mathematical Engineering, Universidad de Chile & Centre for Mathematical Modelling, UMR 2071, Universidad de Chile-CNRS. Casilla 170-3 Santiago 3, Chile&INRIA, Rocquencourt

    Héctor Ramírez C.

Authors
  1. J. Frédéric Bonnans
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  2. Héctor Ramírez C.
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Correspondence to Héctor Ramírez C..

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Dedicated to R.T. Rockafellar on the occasion of his 70th birthday.

Partially supported by Ecos-Conicyt C00E05.

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Bonnans, J., Ramírez C., H. Perturbation analysis of second-order cone programming problems. Math. Program. 104, 205–227 (2005). https://doi.org/10.1007/s10107-005-0613-4

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  • DOI: https://doi.org/10.1007/s10107-005-0613-4

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