A generic coordinate descent solver for non-smooth convex optimisation

Abstract

We present a generic coordinate descent solver for the minimization of a nonsmooth convex objective with structure. The method can deal in particular with problems with linear constraints. The implementation makes use of efficient residual updates and automatically determines which dual variables should be duplicated. A list of basic functional atoms is pre-compiled for efficiency and a modelling language in Python allows the user to combine them at run time. So, the algorithm can be used to solve a large variety of problems including Lasso, sparse multinomial logistic regression, linear and quadratic programs.

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

“…The source code can be found on https: //perso.telecom-paristech.fr/ofercoq/Software.html. It uses the generic primal-dual coordinate descent solver developed in [Fer21]. .…”