# A generic coordinate descent solver for nonsmooth convex optimization

## TL;DR

This paper introduces a versatile coordinate descent solver capable of efficiently handling nonsmooth convex problems with structure, including those with linear constraints, by leveraging residual updates and a flexible modeling language.

## Contribution

The paper presents a generic coordinate descent algorithm with an efficient implementation and a Python-based modeling language, enabling broad applicability to various nonsmooth convex optimization problems.

## Key findings

- Effective for Lasso and sparse logistic regression
- Handles linear and quadratic programming problems
- Automatically manages dual variable duplication

## 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.