matrix optimization – Optimization Online

Proximal Approaches for Matrix Optimization Problems: Application to Robust Precision Matrix Estimation.

Published: 2018/01/23, Updated: 2019/11/14

Applications - OR and Management Sciences bregman divergence, covariance estimation, douglas-rachford method, graphical lasso, majorization-minimization, matrix optimization

In recent years, there has been a growing interest in mathematical mod- els leading to the minimization, in a symmetric matrix space, of a Bregman di- vergence coupled with a regularization term. We address problems of this type within a general framework where the regularization term is split in two parts, one being a spectral … Read more

CONVEX GEOMETRY OF THE GENERALIZED MATRIX-FRACTIONAL FUNCTION

Published: 2017/03/03

James V. Burke

Tim Hoheisel

Yuan Gao

Convex and Nonsmooth Optimization, Convex Optimization, Nonsmooth Optimization gauge function, matrix optimization, matrix-fractional function, support function

Generalized matrix-fractional (GMF) functions are a class of matrix support functions introduced by Burke and Hoheisel as a tool for unifying a range of seemingly divergent matrix optimization problems associated with inverse problems, regularization and learning. In this paper we dramatically simplify the support function representation for GMF functions as well as the representation of … Read more