A fast dual proximal gradient algorithm for convex minimization and applications

Amir Beck; Marc Teboulle

doi:10.1016/j.orl.2013.10.007

A fast dual proximal gradient algorithm for convex minimization and applications

Amir Beck, Marc Teboulle

Tel Aviv University, Technion - Israel Institute of Technology

Research output: Contribution to journal › Article › peer-review

Abstract

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).

Original language	English
Pages (from-to)	1-6
Number of pages	6
Journal	Operations Research Letters
Volume	42
Issue number	1
DOIs	https://doi.org/10.1016/j.orl.2013.10.007
State	Published - 2014

Keywords

Convex optimization
Dual-based methods
Fast gradient methods
Rate of convergence

All Science Journal Classification (ASJC) codes

Software
Management Science and Operations Research
Industrial and Manufacturing Engineering
Applied Mathematics

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10.1016/j.orl.2013.10.007

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title = "A fast dual proximal gradient algorithm for convex minimization and applications",

abstract = "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).",

keywords = "Convex optimization, Dual-based methods, Fast gradient methods, Rate of convergence",

author = "Amir Beck and Marc Teboulle",

note = "Funding Information: The work of Amir Beck partially supported by ISF grant #25312 and the work of Marc Teboulle was partially supported by ISF grant #99812 .",

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AU - Beck, Amir

AU - Teboulle, Marc

N1 - Funding Information: The work of Amir Beck partially supported by ISF grant #25312 and the work of Marc Teboulle was partially supported by ISF grant #99812 .

PY - 2014

Y1 - 2014

N2 - 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).

AB - 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).

KW - Convex optimization

KW - Dual-based methods

KW - Fast gradient methods

KW - Rate of convergence

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U2 - 10.1016/j.orl.2013.10.007

DO - 10.1016/j.orl.2013.10.007

M3 - مقالة

SN - 0167-6377

VL - 42

SP - 1

EP - 6

JO - Operations Research Letters

JF - Operations Research Letters

IS - 1

ER -

A fast dual proximal gradient algorithm for convex minimization and applications

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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