Two Approaches to Solving $l_1$-Regularized Least Squares with Application to Truss Topology Design

Abstract

Many real-world problems may lead to minimization of a non-differentiable convex function of large number of variables. In this paper, we study two different approaches for solving the so-called $l_1$-regularized least squares problem. We apply and compare two competing methods of convex optimization for solving this problem, namely the proximal gradient method and the interior-point method. We describe two specialized inexact interior point methods for solving the $l_1$-regularized least squares problem and compare them with three different versions of the proximal gradient method known from literature. We illustrate performance of these methods on a truss topology design problem with more than 35000 variables. Both methods are compared, analyzed and a discussion on the performance is provided.