Statistical Inference of Second-Order Cone Programming

Jiani Wang and Liwei Zhang ()
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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

Asia-Pacific Journal of Operational Research (APJOR), 2018, vol. 35, issue 06, 1-14

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.

Keywords: Second-order cone programming; the problem of minimizing a sum of weighted norms; constraint nondegeneracy; statistical inference; asymptotics (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1142/S0217595918500446

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