@article {drusvavawolk, title = {Extreme point inequalities and geometry of the rank sparsity ball}, journal = {Mathematical Programming}, volume = {152}, number = {1}, year = {2015}, note = {Arxiv link: }, month = {Aug}, pages = {521{\textendash}544}, abstract = {We investigate geometric features of the unit ball corresponding to the sum of the nuclear norm of a matrix and the \$\$l_1\$\$l1norm of its entries{\textendash}-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.}, issn = {1436-4646}, doi = {10.1007/s10107-014-0795-8}, url = {https://doi.org/10.1007/s10107-014-0795-8}, author = {Drusvyatskiy, D. and Vavasis, S. A. and Wolkowicz, H.} }