Bregman distance regularization for nonsmooth and nonconvex optimization

Abstract

Abstract Solving a nonsmooth and nonconvex minimization problem can be approached as finding a zero of a set-valued operator. With this perspective, we propose a novel Majorizer–Minimizer technique to find a local minimizer of a nonsmooth and nonconvex function and establish its convergence. Our approach leverages Bregman distances to generalize the classical quadratic regularization. By doing so, we generate a family of regularized problems that encompasses quadratic regularization as a special case. To further demonstrate the effectiveness of our method, we apply it on a lasso regression model, showcasing its performance.