Extreme point inequalities and geometry of the rank sparsity ball

Published: 2014/01/19

Convex Optimization compressed sensing, convex analysis, exposed face, nuclear norm, rank, sparsity Short URL: https://optimization-online.org/?p=12727

We investigate geometric features of the unit ball corresponding to the sum of the nuclear norm of a matrix and the l_1 norm of its entries --- a common penalty function encouraging joint low rank and high sparsity. As a byproduct of this effort, we develop a calculus (or algebra) of faces for general convex functions, yielding a simple and unified approach for deriving inequalities balancing the various features of the optimization problem at hand, at the extreme points of the solution set.

Extreme point inequalities and geometry of the rank sparsity ball

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