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Article Dans Une Revue SIAM Journal on Optimization Année : 2019

A Coordinate Descent Primal-Dual Algorithm with Large Step Size and Possibly Non Separable Functions

Résumé

This paper introduces a coordinate descent version of the Vu-Condat algorithm. By coordinate descent, we mean that only a subset of the coordinates of the primal and dual iterates is updated at each iteration, the other coordinates being maintained to their past value. Our method allows us to solve optimization problems with a combination of differentiable functions, constraints as well as non-separable and non-differentiable regularizers. We show that the sequences generated by our algorithm converge to a saddle point of the problem at stake, for a wider range of parameter values than previous methods. In particular, the condition on the step-sizes depends on the coordinate-wise Lipschitz constant of the differentiable function's gradient, which is a major feature allowing classical coordinate descent to perform so well when it is applicable. We illustrate the performances of the algorithm on a total-variation regularized least squares regression problem and on large scale support vector machine problems.
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Dates et versions

hal-01497104 , version 1 (28-03-2017)
hal-01497104 , version 2 (05-02-2019)

Identifiants

Citer

Olivier Fercoq, Pascal Bianchi. A Coordinate Descent Primal-Dual Algorithm with Large Step Size and Possibly Non Separable Functions. SIAM Journal on Optimization, 2019, 29 (1), pp.100-134. ⟨hal-01497104v2⟩
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