A New Projected Quasi-Newton Approach for the Nonnegative Least Squares Problem

Constrained least squares estimation lies at the heart of many applications in fields as diverse as statistics, psychometrics, signal processing, or even machine learning. Nonnegativity requirements on the model variables are amongst the simplest constraints that arise naturally, and the corresponding least-squares problem is called Nonnegative Least Squares or NNLS. In this paper we present a new, efficient, and scalable Quasi-Newton-type method for solving the NNLS problem, improving on several previous approaches and leading to a superlinearly convergent method. We show experimental results comparing our method to well-known methods for solving the NNLS problem. Our method significantly outperforms other methods, especially as the problem size becomes larger.