Release Time:2019-10-19  Hits:

Indexed by: Journal Article

Date of Publication: 2015-01-01

Journal: 中国运筹学会会刊

Included Journals: Scopus、CSCD、EI

Volume: 3

Issue: 3

Page Number: 275-296

ISSN: 2194-668X

Abstract: 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.