A smoothing Newton method for mathematical programs governed by second‐order cone constrained generalized equations

A smoothing Newton method for mathematical programs governed by second‐order cone constrained generalized equations

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Article ID: iaor20131209
Volume: 55
Issue: 2
Start Page Number: 359
End Page Number: 385
Publication Date: Feb 2013
Journal: Journal of Global Optimization
Authors: , ,
Keywords: programming: mathematical
Abstract:

In this paper, we consider a class of mathematical programs governed by second‐order cone constrained parameterized generalized equations. We reformulate the necessary optimality conditions as a system of nonsmooth equations under linear independence constraint qualification and the strict complementarity condition. A set of second order sufficient conditions is proposed, which is proved to be sufficient for the second order growth of the stationary point. The smoothing Newton method in [40] is employed to solve the system of nonsmooth equations whose strongly BD‐regularity at a solution point is demonstrated under the second order sufficient conditions. Several illustrative examples are provided and discussed.

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