Characterizations of local upper Lipschitz property of perturbed solutions to nonlinear second-order cone programs. (3rd July 2017)

• Record Type: Journal Article
• Authors: Zhang, Yi; Zhang, Liwei; Wu, Jia; Wang, Keding
• Is Part Of: Optimization. Volume 66:Number 7(2017)
• Page Start: 1079
• Page End: 1103
• Publication Date: 2017-07-03
• Subjects: Second-order cone program -- local upper Lipschitz property -- graphical derivative -- second-order sufficient condition -- strict constraint qualification; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2017.1325887
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : We characterize the local upper Lipschitz property of the stationary point mapping and the Karush–Kuhn–Tucker (KKT) mapping for a nonlinear second-order cone programming problem using the graphical derivative criterion. We demonstrate that the second-order sufficient condition and the strict constraint qualification are sufficient for the local upper Lipschitz property of the stationary point mapping and are both sufficient and necessary for the local upper Lipschitz property of the KKT mapping.