In this paper we consider distributed optimization problems in which the cost function is separable (i.e., a sum of possibly non-smooth functions all sharing a common variable) and can be split into a strongly convex term and a convex one. The second term is typically used to encode constraints or to regularize the solution. We propose an asynchronous, distributed optimization algorithm over an undirected topology, based on a proximal gradient update on the dual problem. We show that by means of a proper choice of primal variables, the dual problem is separable and the dual variables can be stacked into separate blocks. This allows us to show that a distributed gossip update can be obtained by means of a randomized block-coordinate proximal gradient on the dual function.
Randomized dual proximal gradient for large-scale distributed optimization / Notarnicola Ivano; Notarstefano Giuseppe. - ELETTRONICO. - (2015), pp. 712-717. (Intervento presentato al convegno 54th IEEE Conference on Decision and Control tenutosi a Osaka, Japan nel 15-18 Dec. 2015) [10.1109/CDC.2015.7402313].
Randomized dual proximal gradient for large-scale distributed optimization
Notarnicola Ivano
;Notarstefano Giuseppe
2015
Abstract
In this paper we consider distributed optimization problems in which the cost function is separable (i.e., a sum of possibly non-smooth functions all sharing a common variable) and can be split into a strongly convex term and a convex one. The second term is typically used to encode constraints or to regularize the solution. We propose an asynchronous, distributed optimization algorithm over an undirected topology, based on a proximal gradient update on the dual problem. We show that by means of a proper choice of primal variables, the dual problem is separable and the dual variables can be stacked into separate blocks. This allows us to show that a distributed gossip update can be obtained by means of a randomized block-coordinate proximal gradient on the dual function.File | Dimensione | Formato | |
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