Characterizations of local upper Lipschitz property of perturbed solutions to nonlinear second-order cone programs

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.

Keywords:

• Second-order cone program
• local upper Lipschitz property
• graphical derivative
• second-order sufficient condition
• strict constraint qualification

Acknowledgements

The authors are grateful to the editor and the anonymous referee for their valuable comments on this paper.

Notes

All the authors have no conflict of interest.

Additional information

Funding

The research was partly supported by the National Natural Science Foundation of China [project number 11401210], [project number 11671183], [project number 11571059], [project number 91330206], [project number 11301049].