Playing with Duality: An Overview of Recent Primal-Dual Approaches for Solving Large-Scale Optimization Problems

Abstract : Optimization methods are at the core of many problems in signal/image processing, computer vision, and machine learning.For a long time, it has been recognized that looking at the dual of an optimization problem may drastically simplify its solution.Deriving efficient strategies which jointly brings into play the primal and the dual problems is however a more recent idea which has generated many important new contributions in the last years. These novel developments are grounded on recent advances in convex analysis, discrete optimization, parallel processing, and nonsmooth optimization with emphasis on sparsity issues.In this paper, we aim at presenting the principles of primal-dual approaches, while giving an overview of numerical methods which have been proposed in different contexts. We show the benefits which can be drawn from primal-dual algorithms both for solving large-scale convex optimization problems and discrete ones, and we provide various application examples to illustrate their usefulness.
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https://hal.archives-ouvertes.fr/hal-01010437
Contributeur : Nikos Komodakis <>
Soumis le : mercredi 3 décembre 2014 - 23:20:05
Dernière modification le : samedi 11 février 2017 - 01:06:37
Document(s) archivé(s) le : lundi 9 mars 2015 - 05:53:44

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  • HAL Id : hal-01010437, version 2

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Nikos Komodakis, Jean-Christophe Pesquet. Playing with Duality: An Overview of Recent Primal-Dual Approaches for Solving Large-Scale Optimization Problems. 2014. <hal-01010437v2>

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