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论文类型：期刊论文

发表时间：2015-01-01

发表刊物：中国运筹学会会刊

收录刊物：EI、CSCD、Scopus

卷号：3

期号：3

页面范围：275-296

ISSN号：2194-668X

摘要：In this paper, we consider a cone problem of matrix optimization induced by spectral norm (MOSN). By Schur complement, MOSN can be reformulated as a nonlinear semidefinite programming (NLSDP) problem. Then we discuss the constraint nondegeneracy conditions and strong second-order sufficient conditions of MOSN and its SDP reformulation, and obtain that the constraint nondegeneracy condition of MOSN is not always equivalent to that of NLSDP. However, the strong second-order sufficient conditions of these two problems are equivalent without any assumption. Finally, a sufficient condition is given to ensure the nonsingularity of the Clarke  s generalized Jacobian of the KKT system for MOSN. ? 2015, Operations Research Society of China, Periodicals Agency of Shanghai University, Science Press and Springer-Verlag Berlin Heidelberg.