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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Journal of the Operations Research Society of China
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
