A second-order method for convex ℓ1-regularized optimization with active-set prediction

N. Keskar*, J. Nocedal, F. Öztoprak, A. Wächter

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


We describe an active-set method for the minimization of an objective function that is the sum of a smooth convex function f and an-regularization term. A distinctive feature of the method is the way in which active-set identification and second-order subspace minimization steps are integrated to combine the predictive power of the two approaches. At every iteration, the algorithm selects a candidate set of free and fixed variables, performs an (inexact) subspace phase, and then assesses the quality of the new active set. If it is not judged to be acceptable, then the set of free variables is restricted and a new active-set prediction is made. We establish global convergence for our approach under the assumptions of Lipschitz-continuity and strong-convexity of f, and compare the new method against state-of-the-art codes.

Original languageEnglish (US)
Pages (from-to)605-621
Number of pages17
JournalOptimization Methods and Software
Issue number3
StatePublished - May 3 2016


  • active-set correction
  • active-set prediction
  • second-order
  • subspaceoptimization
  • ℓ-minimization

ASJC Scopus subject areas

  • Software
  • Control and Optimization
  • Applied Mathematics


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