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Statistical Inference of Second-Order Cone Programming

Author

Listed:
  • Jiani Wang

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

  • Liwei Zhang

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

Abstract

The randomness of the second-order cone programming problems is mainly reflected in the objective function and the constraints both having random vectors. In this paper, we discuss the statistical properties of estimates of the respective optimal value and optimal solutions when the random vectors are estimated by their sample both in the objective function and the constraints, which are based on perturbation analysis theory of second-order cone programming. As an example we consider the problem of minimizing a sum of norms with weights.

Suggested Citation

  • Jiani Wang & Liwei Zhang, 2018. "Statistical Inference of Second-Order Cone Programming," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 35(06), pages 1-14, December.
    • Handle: RePEc:wsi:apjorx:v:35:y:2018:i:06:n:s0217595918500446
    DOI: 10.1142/S0217595918500446
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    References listed on IDEAS

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    1. J. Frédéric Bonnans & Roberto Cominetti & Alexander Shapiro, 1998. "Sensitivity Analysis of Optimization Problems Under Second Order Regular Constraints," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 806-831, November.
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