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Statistical Inference of Second-Order Cone Programming

Author

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  • Liwei Zhang

    (The School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, P. R. China)

  • Shengzhe Gao

    (The School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, P. R. China2The School of Science, Dalian Ocean University, Dalian 116023, P. R. China)

  • Saoyan Guo

    (The School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, P. R. China)

Abstract

In this paper, we study the stability of stochastic second-order programming when the probability measure is perturbed. Under the Lipschitz continuity of the objective function and metric regularity of the feasible set-valued mapping, the outer semicontinuity of the optimal solution set and Lipschitz continuity of optimal values are demonstrated. Moreover, we prove that, if the constraint non-degeneracy condition and strong second-order sufficient condition hold at a local minimum point of the original problem, there exists a Lipschitz continuous solution path satisfying the Karush–Kuhn–Tucker conditions.

Suggested Citation

  • Liwei Zhang & Shengzhe Gao & Saoyan Guo, 2019. "Statistical Inference of Second-Order Cone Programming," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 36(02), pages 1-17, April.
    • Handle: RePEc:wsi:apjorx:v:36:y:2019:i:02:n:s0217595919400037
    DOI: 10.1142/S0217595919400037
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    References listed on IDEAS

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    1. Yun Wang & Liwei Zhang, 2009. "Properties of equation reformulation of the Karush–Kuhn–Tucker condition for nonlinear second order cone optimization problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 70(2), pages 195-218, October.
    2. Defeng Sun, 2006. "The Strong Second-Order Sufficient Condition and Constraint Nondegeneracy in Nonlinear Semidefinite Programming and Their Implications," Mathematics of Operations Research, INFORMS, vol. 31(4), pages 761-776, November.
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