- A Family of Second-Order Methods for Convex L1-Regularized Optimization Richard H Byrd(richard.byrdcolorado.edu) Gillian M Chin(gillian.chinu.northwestern.edu) Jorge Nocedal(nocedaleecs.northwestern.edu) Figen Oztoprak(figensabanciuniv.edu) Abstract: This paper is concerned with the minimization of an objective that is the sum of a convex function $f$ and an $\ell_1$ regularization term. Our interest is in methods that incorporate second-order information about the function $f$ to accelerate convergence. We describe a semi-smooth Newton framework that can be used to generate a variety of second-order methods, including block active-set methods, orthant-based methods and a second-order iterative soft-thresholding method. We also propose a new active set method that performs multiple changes in the active manifold estimate, and incorporates a novel mechanism for correcting estimates, when needed. This corrective mechanism is also evaluated in an orthant-based method. Numerical tests comparing the performance of several second-order methods are presented. Keywords: semi-smooth Newton, L1-regularization, quadratic programming Category 1: Convex and Nonsmooth Optimization Category 2: Nonlinear Optimization Citation: Unpublished: Optimization Center: Northwestern University, Tech Report, June 2012 Download: [PDF]Entry Submitted: 06/26/2012Entry Accepted: 06/26/2012Entry Last Modified: 06/26/2012Modify/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.