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CORR
2012
Springer

On the Lagrangian Biduality of Sparsity Minimization Problems

8 years 5 months ago
On the Lagrangian Biduality of Sparsity Minimization Problems
We present a novel primal-dual analysis on a class of NPhard sparsity minimization problems to provide new interpretations for their well known convex relaxations. We show that the Lagrangian bidual (i.e., the Lagrangian dual of the Lagrangian dual) of the sparsity minimization problems can be used to derive interesting convex relaxations: the bidual of the 0-minimization problem is 1-minimization; and the bidual of 0,1-minimization for enforcing group sparsity on structured data is 1,∞-minimization problem. Intuitions from the bidual-based relaxation are used to introduce a new family of relaxations for the group sparsity minimization problem.
Dheeraj Singaraju, Ehsan Elhamifar, Roberto Tron,
Added 20 Apr 2012
Updated 20 Apr 2012
Type Journal
Year 2012
Where CORR
Authors Dheeraj Singaraju, Ehsan Elhamifar, Roberto Tron, Allen Y. Yang, Shankar S. Sastry
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