A dual method for minimizing a nonsmooth objective over one smooth inequality constraint

Ron Shefi, Marc Teboulle*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We consider the class of nondifferentiable convex problems which minimizes a nonsmooth convex objective over a single smooth constraint. Exploiting the smoothness of the feasible set and using duality, we introduce a simple first order algorithm proven to globally converge to an optimal solution with a O(1 / ε) efficiency estimate. The performance of the algorithm is demonstrated by solving large instances of the convex sparse recovery problem.

Original languageEnglish
Pages (from-to)137-164
Number of pages28
JournalMathematical Programming
Volume159
Issue number1-2
DOIs
StatePublished - 1 Sep 2016

Keywords

  • Complexity/rate of convergence analysis
  • Duality
  • First order methods
  • Nonsmooth convex minimization
  • Sparse recovery
  • l-norm minimization

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