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论文类型：期刊论文
发表时间：2016-04-01
发表刊物：ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH
收录刊物：SCIE、EI、Scopus
卷号：33
期号：2
ISSN号：0217-5959
关键字：Nuclear norm; second-order tangent set; sigma term; no gap second-order optimality conditions
摘要：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.