A smoothing Newton method for mathematical programs governed by second-order cone constrained generalized equations |
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Authors: | Jia Wu Liwei Zhang Yi Zhang |
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Affiliation: | 1. School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, China
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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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