A survey on operator splitting and decomposition of convex programs

Lenoir, Arnaud; Mahey, Philippe

RAIRO - Operations Research - Recherche Opérationnelle, Tome 51 (2017) no. 1, pp. 17-41.

Many structured convex minimization problems can be modeled by the search of a zero of the sum of two monotone operators. Operator splitting methods have been designed to decompose and regularize at the same time these kind of models. We review here these models and the classical splitting methods. We focus on the numerical sensitivity of these algorithms with respect to the scaling parameters that drive the regularizing terms, in order to accelerate convergence rates for different classes of models.

Classification : 65K13, 90C25, 90C30
Mots clés : Operator splitting, Augmented Lagrangian, Decomposition methods

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