Abstract
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 language | English (US) |
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Pages (from-to) | 605-621 |
Number of pages | 17 |
Journal | Optimization Methods and Software |
Volume | 31 |
Issue number | 3 |
DOIs | |
State | Published - May 3 2016 |
Funding
Authors (N.K. and A.W.) were partially supported by the National Science Foundation grant DMS-1216920. Authors (N.K. and J.N.) were partially supported by National Science Foundation grant DMS-1216567 and Office of Naval Research award N000141410313. Author (F.O.) was supported by the Scientific and Technological Research Council of Turkey grant #113M500 and U.S. Department of Energy Award Number FG02-87ER25047.
Keywords
- active-set correction
- active-set prediction
- second-order
- subspaceoptimization
- ℓ-minimization
ASJC Scopus subject areas
- Software
- Control and Optimization
- Applied Mathematics