On the Aubin Property of Critical Points to Perturbed Second-Order Cone Programs

On the Aubin Property of Critical Points to Perturbed Second-Order Cone Programs

We characterize the Aubin property of a canonically perturbed KKT system related to the second-order cone programming problem in terms of a strong second-order optimality condition. This condition requires the positive definiteness of a quadratic form, involving the Hessian of the Lagrangian and an...

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Veröffentlicht in:SIAM journal on optimization 2011-07, Vol.21 (3), p.798-823
Hauptverfasser: Outrata, Jiří V., Ramírez C., Héctor
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Algebra
Applied mathematics
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description We characterize the Aubin property of a canonically perturbed KKT system related to the second-order cone programming problem in terms of a strong second-order optimality condition. This condition requires the positive definiteness of a quadratic form, involving the Hessian of the Lagrangian and an extra term, associated with the curvature of the constraint set, over the linear space generated by the cone of critical directions. Since this condition is equivalent with the Robinson strong regularity, the mentioned KKT system behaves (with some restrictions) similarly as in nonlinear programming. [PUBLICATION ABSTRACT]
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Applied mathematics
title On the Aubin Property of Critical Points to Perturbed Second-Order Cone Programs
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