No Gap Second-order Optimality Conditions for a Matrix Cone Programming Induced by the Nuclear Norm

Ning Zhang and Liwei Zhang ()
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Ning Zhang: Institute of Operations Research and Control Theory, School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, P. R. China
Liwei Zhang: Institute of Operations Research and Control Theory, School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, P. R. China

Asia-Pacific Journal of Operational Research (APJOR), 2016, vol. 33, issue 02, 1-20

Abstract: The first-order and the second-order directional derivatives of singular values are used to characterize the tangent cone, the normal cone and the second-order tangent set of the epigraph of the nuclear norm of matrices. Based on the variational geometry of the epigraph, the no gap second-order optimality conditions for the optimization problem, whose constraint is defined by the matrix cone induced by the nuclear norm, are established.

Keywords: Nuclear norm; second-order tangent set; sigma term; no gap second-order optimality conditions (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1142/S021759591650010X

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