Perturbation analysis of second-order cone programming problems

Authors:
J. Frédéric Bonnans;Héctor Ramírez C.
Affiliations:
Projet Sydoco, INRIA Rocquencourt, B.P. 105, Le Chesnay, France;Department of Mathematical Engineering, Universidad de Chile & Centre for Mathematical Modelling, UMR 2071, Universidad de Chile-CNRS. Casilla 170-3 Santiago 3, Chile&INRIA, B.P. 105, Le Chesnay, ...
Venue:
Mathematical Programming: Series A and B
Year:
2005

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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.