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Playing with duality: An overview of recent primaldual approaches for . . .
, 2014
"... 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 jointly bringing i ..."
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Cited by 5 (1 self)
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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 jointly bringing 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 primaldual approaches, while giving an overview of numerical methods which have been proposed in different contexts. We show the benefits which can be drawn from primaldual algorithms both for solving largescale convex optimization problems and discrete ones, and we provide various application examples to illustrate their usefulness.
A Class of Randomized PrimalDual Algorithms for Distributed Optimization, arXiv preprint arXiv:1406.6404v3
, 2014
"... Abstract Based on a preconditioned version of the randomized blockcoordinate forwardbackward algorithm recently proposed in ..."
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Abstract Based on a preconditioned version of the randomized blockcoordinate forwardbackward algorithm recently proposed in
Best Approximation from the KuhnTucker Set of Composite Monotone Inclusions
"... KuhnTucker points play a fundamental role in the analysis and the numerical solution of monotone inclusion problems, providing in particular both primal and dual solutions. We propose a class of strongly convergent algorithms for constructing the best approximation to a reference point from the set ..."
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KuhnTucker points play a fundamental role in the analysis and the numerical solution of monotone inclusion problems, providing in particular both primal and dual solutions. We propose a class of strongly convergent algorithms for constructing the best approximation to a reference point from the set of KuhnTucker points of a general Hilbertian composite monotone inclusion problem. Applications to systems of coupled monotone inclusions are presented. Our framework does not impose additional assumptions on the operators present in the formulation or knowledge of the norm of the linear operators.
PrimalDual Approaches for Solving LargeScale Optimization Problems
, 2014
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