A simple algorithm for a class of nonsmooth convex-concave saddle-point problems

Yoel Drori; Shoham Sabach; Marc Teboulle

doi:10.1016/j.orl.2015.02.001

A simple algorithm for a class of nonsmooth convex-concave saddle-point problems

Yoel Drori, Shoham Sabach, Marc Teboulle

Technion - Israel Institute of Technology, Tel Aviv University

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

Abstract

We introduce a novel algorithm for solving a class of structured nonsmooth convex-concave saddle-point problems involving a smooth function and a sum of finitely many bilinear terms and nonsmooth functions. The proposed method is simple and proven to globally converge to a saddle-point with an O(1/ε) efficiency estimate. We demonstrate its usefulness for tackling a broad class of minimization models with a finitely sum of composite nonsmooth functions.

Original language	English
Pages (from-to)	209-214
Number of pages	6
Journal	Operations Research Letters
Volume	43
Issue number	2
DOIs	https://doi.org/10.1016/j.orl.2015.02.001
State	Published - Mar 2015

Keywords

Iteration complexity
Nonsmooth convex minimization
Saddle-point problems

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.2015.02.001

Cite this

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abstract = "We introduce a novel algorithm for solving a class of structured nonsmooth convex-concave saddle-point problems involving a smooth function and a sum of finitely many bilinear terms and nonsmooth functions. The proposed method is simple and proven to globally converge to a saddle-point with an O(1/ε) efficiency estimate. We demonstrate its usefulness for tackling a broad class of minimization models with a finitely sum of composite nonsmooth functions.",

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N2 - We introduce a novel algorithm for solving a class of structured nonsmooth convex-concave saddle-point problems involving a smooth function and a sum of finitely many bilinear terms and nonsmooth functions. The proposed method is simple and proven to globally converge to a saddle-point with an O(1/ε) efficiency estimate. We demonstrate its usefulness for tackling a broad class of minimization models with a finitely sum of composite nonsmooth functions.

AB - We introduce a novel algorithm for solving a class of structured nonsmooth convex-concave saddle-point problems involving a smooth function and a sum of finitely many bilinear terms and nonsmooth functions. The proposed method is simple and proven to globally converge to a saddle-point with an O(1/ε) efficiency estimate. We demonstrate its usefulness for tackling a broad class of minimization models with a finitely sum of composite nonsmooth functions.

KW - Iteration complexity

KW - Nonsmooth convex minimization

KW - Saddle-point problems

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DO - 10.1016/j.orl.2015.02.001

M3 - مقالة

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JO - Operations Research Letters

JF - Operations Research Letters

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A simple algorithm for a class of nonsmooth convex-concave saddle-point problems

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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