Extreme point inequalities and geometry of the rank sparsity ball
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 c...
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| Veröffentlicht in: | Mathematical programming 2015-08, Vol.152 (1-2), p.521-544 |
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| creator | Drusvyatskiy, D. Vavasis, S. A. Wolkowicz, H. |
| description | 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. |
| doi_str_mv | 10.1007/s10107-014-0795-8 |
| format | Article |
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l
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l
1
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| subjects | Balancing Byproducts Calculus Calculus of Variations and Optimal Control Optimization Combinatorics Convex analysis Full Length Paper Functions (mathematics) Geometry Inequalities Mathematical analysis Mathematical and Computational Physics Mathematical Methods in Physics Mathematical models Mathematical programming Mathematics Mathematics and Statistics Mathematics of Computing Norms Numerical Analysis Optimization Sparsity Studies Texts Theoretical |
| title | Extreme point inequalities and geometry of the rank sparsity ball |
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