L1Packv2: A Mathematica package for minimizing an $\ell_1$-penalized functional

TL;DR

L1Packv2 is a Mathematica package offering algorithms for minimizing an $ ext{L}_1$-penalized least squares functional, capable of handling mixed variables and providing exact solutions with precise data.

Contribution

It introduces a comprehensive Mathematica package with algorithms for $ ext{L}_1$-penalized minimization, including exact data handling and illustrative examples.

Findings

Algorithms handle mixed penalized and unpenalized variables.

Provides exact solutions with exact input data.

Includes instructive examples for users.

Abstract

L1Packv2 is a Mathematica package that contains a number of algorithms that can be used for the minimization of an $\ell_1$-penalized least squares functional. The algorithms can handle a mix of penalized and unpenalized variables. Several instructive examples are given. Also, an implementation that yields an exact output whenever exact data are given is provided.