Section: New Results

Proximal Approaches for Solving Matrix Optimization Problems

Participants: Emilie Chouzenoux and Jean-Christophe Pesquet (in collaboration with A. Benfenati, Univ. Paris Est)

In recent years, there has been a growing interest in problems where the underlining mathematical model involves the minimization in a matrix space of a Bregman divergence function coupled with a regularization term. We consider a general framework where the regularization term is decoupled in two parts, one acting only on the eigenvalues of the matrix and the other on the whole matrix. We propose in [26], [32] a new minimization approach to address problem of this type, by providing a list of proximity operators allowing us to consider various choices for the fit–to–data functional and for the regularization term. The numerical experience show that this approach gives better results in term of computational time with respect to some state of the arts algorithms.