Convex Geometry of the Generalized Matrix-Fractional Function
This work provides tools for unifying matrix optimization problems in inverse problems, regularization, and learning, but it appears incremental as it focuses on simplifying existing representations.
The paper tackled the complexity of representing generalized matrix-fractional functions and their subdifferentials, resulting in simplified representations that enable computation of previously unavailable geometric objects.
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 their subdifferentials. These new representations allow the ready computation of a range of important related geometric objects whose formulations were previously unavailable.