The Proximal Alternating Minimization Algorithm for Two-Block Separable Convex Optimization Problems with Linear Constraints

Sandy Bitterlich (), Radu Ioan Boţ (), Ernö Robert Csetnek () and Gert Wanka ()
Additional contact information
Sandy Bitterlich: Chemnitz University of Technology
Radu Ioan Boţ: University of Vienna
Ernö Robert Csetnek: University of Vienna
Gert Wanka: Chemnitz University of Technology

Journal of Optimization Theory and Applications, 2019, vol. 182, issue 1, No 6, 110-132

Abstract: Abstract The Alternating Minimization Algorithm has been proposed by Paul Tseng to solve convex programming problems with two-block separable linear constraints and objectives, whereby (at least) one of the components of the latter is assumed to be strongly convex. The fact that one of the subproblems to be solved within the iteration process of this method does not usually correspond to the calculation of a proximal operator through a closed formula affects the implementability of the algorithm. In this paper, we allow in each block of the objective a further smooth convex function and propose a proximal version of the algorithm, which is achieved by equipping the algorithm with proximal terms induced by variable metrics. For suitable choices of the latter, the solving of the two subproblems in the iterative scheme can be reduced to the computation of proximal operators. We investigate the convergence of the proposed algorithm in a real Hilbert space setting and illustrate its numerical performances on two applications in image processing and machine learning.

Keywords: Proximal AMA; Lagrangian; Saddle points; Subdifferential; Convex optimization; Fenchel duality; 47H05; 65K05; 90C25 (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10957-018-01454-y Abstract (text/html)
Access to the full text of the articles in this series is restricted.

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:joptap:v:182:y:2019:i:1:d:10.1007_s10957-018-01454-y

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-018-01454-y

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

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