- An Inexact Successive Quadratic Approximation Method for Convex L-1 Regularized Optimization Richard Byrd(richardcs.colorado.edu) Jorge Nocedal(nocedaleecs.northwestern.edu) Figen Oztoprak(figensabanciuniv.edu) Abstract: We study a Newton-like method for the minimization of an objective function $\phi$ that is the sum of a smooth convex function and an $\ell_1$ regularization term. This method, which is sometimes referred to in the literature as a proximal Newton method, computes a step by minimizing a piecewise quadratic model $q_k$ of the objective function $\phi$. In order to make this approach efficient in practice, it is imperative to perform this inner minimization inexactly. In this paper, we give inexactness conditions that guarantee global convergence and that can be used to control the local rate of convergence of the iteration. Our inexactness conditions are based on a semi-smooth function that represents a (continuous) measure of the optimality conditions of the problem, and that embodies the soft-thresholding iteration. We give careful consideration to the algorithm employed for the inner minimization, and report numerical results on two test sets originating in machine learning. Keywords: convex optimization, inexact proximal Newton method Category 1: Convex and Nonsmooth Optimization Category 2: Nonlinear Optimization Citation: Report 05 Optimization Center Northwestern University Download: [PDF]Entry Submitted: 09/09/2013Entry Accepted: 09/09/2013Entry Last Modified: 09/09/2013Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.