On certain optimization problems related to matrix norms. (2nd October 2016)

• Record Type: Journal Article
• Authors: Wei, Ning
• Is Part Of: Optimization. Volume 65:Number 10(2016)
• Page Start: 1791
• Page End: 1803
• Publication Date: 2016-10-02
• Subjects: Convex programming -- unitarily invariant norm -- optimization problem -- matrix norm; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2016.1217860
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In this paper, first, we show that the following optimization problem always has an optimal solution which does not depend on the matrix norm, and give a sufficient condition for the uniqueness of optimal solutions: (Section.Display) where is any unitarily invariant norm, , and or . Then, we characterize the optimal solutions and also give sufficient conditions for the uniqueness and the rank-one property of optimal solutions for the following optimization problem: (Section.Display) where, is the inner product of matrices;, , , and 's, are different arbitrary norms.