A fast dual proximal gradient algorithm for convex minimization and applications

We consider the convex composite problem of minimizing the sum of a strongly convex function and a general extended valued convex function. We present a dual-based proximal gradient scheme for solving this problem. We show that although the rate of convergence of the dual objective function sequence...

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Bibliographic Details
Published in:Operations research letters Vol. 42; no. 1; pp. 1 - 6
Main Authors: Beck, Amir, Teboulle, Marc
Format: Journal Article
Language:English
Published: Elsevier B.V 01.01.2014
Subjects:
Algorithms
Convergence
Convex optimization
Dual-based methods
Fast gradient methods
Minimization
Operations research
Optimization
Rate of convergence
Sequences
Fast gradient methods
Dual-based methods
Rate of convergence
Convex optimization
ISSN:0167-6377, 1872-7468
Online Access:Get full text
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Summary:We consider the convex composite problem of minimizing the sum of a strongly convex function and a general extended valued convex function. We present a dual-based proximal gradient scheme for solving this problem. We show that although the rate of convergence of the dual objective function sequence converges to the optimal value with the rate O(1/k2), the rate of convergence of the primal sequence is of the order O(1/k).
Bibliography:ObjectType-Article-1
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ISSN:0167-6377
1872-7468
DOI:10.1016/j.orl.2013.10.007