The Lawson-Hanson Algorithm with Deviation Maximization: Finite Convergence and Sparse Recovery

TL;DR

This paper introduces LHDM, a new algorithm for NonNegative Least Squares that uses deviation maximization, achieving finite convergence, improved performance through BLAS-3 operations, and effective sparse recovery demonstrated by extensive experiments.

Contribution

The paper proposes LHDM, a novel NNLS algorithm incorporating deviation maximization, with proven finite convergence and enhanced sparse recovery capabilities.

Findings

LHDM converges finitely for NNLS problems.

LHDM outperforms several $ ext{l}_1$-minimization solvers in experiments.

LHDM benefits from BLAS-3 operations for higher computational efficiency.

Abstract

In this work we apply the "deviation maximization", a new column selection strategy, to the Lawson-Hanson algorithm for the solution of NonNegative Least Squares (NNLS), devising a new algorithm we call Lawson-Hanson with Deviation Maximization (LHDM). This algorithm allows to exploit BLAS-3 operations, leading to higher performances. We show the finite convergence of this algorithm and explore the sparse recovery ability of LHDM. The results are presented with an extensive campaign of experiments, where we compare its performance against several $\ell_1$-minimization solvers. An implementation of the proposed algorithm is available on a public repository.