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CONVEX GEOMETRY OF THE GENERALIZED MATRIX-FRACTIONAL FUNCTION

James Burke(jvburke***at***uw.edu)
Yuan Gao(yuangao***at***uw.edu)
Tim Hoheisel(tim.hoheisel***at***mcgill.ca)

Abstract: 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.

Keywords: matrix optimization, matrix-fractional function, support function, gauge function

Category 1: Convex and Nonsmooth Optimization

Category 2: Convex and Nonsmooth Optimization (Convex Optimization )

Category 3: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Citation: Submitted; University of Washington, McGill University; 03/2017

Download: [PDF]

Entry Submitted: 03/03/2017
Entry Accepted: 03/03/2017
Entry Last Modified: 03/03/2017

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