Mirror Prox algorithm for multi-term composite minimization and semi-separable problems

Niao He (), Anatoli Juditsky () and Arkadi Nemirovski ()

Computational Optimization and Applications, 2015, vol. 61, issue 2, 275-319

Abstract: In the paper, we develop a composite version of Mirror Prox algorithm for solving convex–concave saddle point problems and monotone variational inequalities of special structure, allowing to cover saddle point/variational analogies of what is usually called “composite minimization” (minimizing a sum of an easy-to-handle nonsmooth and a general-type smooth convex functions “as if” there were no nonsmooth component at all). We demonstrate that the composite Mirror Prox inherits the favourable (and unimprovable already in the large-scale bilinear saddle point case) [InlineEquation not available: see fulltext.] efficiency estimate of its prototype. We demonstrate that the proposed approach can be successfully applied to Lasso-type problems with several penalizing terms (e.g. acting together $$\ell _1$$ ℓ 1 and nuclear norm regularization) and to problems of semi-separable structures considered in the alternating directions methods, implying in both cases methods with the [InlineEquation not available: see fulltext.] complexity bounds. Copyright Springer Science+Business Media New York 2015

Keywords: Numerical algorithms for variational problems; Composite optimization; Minimization problems with multi-term penalty; Proximal methods; 65K10; 65K05; 90C06; 90C25; 90C47 (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://hdl.handle.net/10.1007/s10589-014-9723-3 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:coopap:v:61:y:2015:i:2:p:275-319

Ordering information: This journal article can be ordered from
http://www.springer.com/math/journal/10589

DOI: 10.1007/s10589-014-9723-3

Access Statistics for this article

Computational Optimization and Applications is currently edited by William W. Hager

More articles in Computational Optimization and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().