Convex analysis on the Hermitian matrices. (English) Zbl 0849.15013
From the author’s abstract: It is known that convex spectral functions can be characterized exactly as symmetric convex functions of the eigenvalues. A new approach to this characterization is given, via a simple Fenchel conjugacy formula. We then apply this formula to derive expressions for subdifferentials, and to study duality relationships for convex optimization problems with positive semidefinite matrices as variables. Analogous results hold for Hermitian matrices.
Reviewer: L.Elsner (Bielefeld)
MSC:
15A45 | Miscellaneous inequalities involving matrices |
90C25 | Convex programming |
65K05 | Numerical mathematical programming methods |