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: | Zhang Yi, Zhang Liwei, Wu Jia |
Keywords: | programming: mathematical |
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.