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

Indexed by:期刊论文

Journal:JOURNAL OF GLOBAL OPTIMIZATION

Included Journals:SCIE、EI、Scopus

Volume:55

Issue:2

Page Number:359-385

ISSN No.:0925-5001

Key Words:Smoothing Newton method; Generalized equations; Second-order cone; MPEC; Optimality conditions

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.

Date of Publication:2013-02-01