Performance of First- and Second-Order Methods for L1-Regularized Least Squares Problems

TL;DR

This paper evaluates how first- and second-order optimization methods perform on large-scale L1-regularized least squares problems, considering factors like conditioning and problem size up to one trillion, using a scalable generator.

Contribution

It introduces a low-memory, scalable generator for creating large sparse L1-regularized problems with controllable parameters, enabling extensive performance testing.

Findings

Performance varies with problem conditioning and size

The generator efficiently produces large-scale test problems

Insights into optimization method scalability and robustness

Abstract

We study the performance of first- and second-order optimization methods for l1-regularized sparse least-squares problems as the conditioning of the problem changes and the dimensions of the problem increase up to one trillion. A rigorously defined generator is presented which allows control of the dimensions, the conditioning and the sparsity of the problem. The generator has very low memory requirements and scales well with the dimensions of the problem.