- Geometric descent method for convex composite minimization Shixiang Chen (sxchense.cuhk.edu.hk) Shiqian Ma (sqmase.cuhk.edu.hk) Wei Liu (wliuee.columbia.edu) Abstract: In this paper, we extend the geometric descent method recently proposed by Bubeck, Lee and Singh to tackle nonsmooth and strongly convex composite problems. We prove that our proposed algorithm, dubbed geometric proximal gradient method (GeoPG), converges with a linear rate $(1-1/\sqrt{\kappa})$ and thus achieves the optimal rate among first-order methods, where $\kappa$ is the condition number of the problem. Numerical results on linear regression and logistic regression with elastic net regularization show that GeoPG compares favorably with Nesterov's accelerated proximal gradient method, especially when the problem is ill-conditioned. Keywords: Category 1: Convex and Nonsmooth Optimization Citation: Download: [PDF]Entry Submitted: 01/03/2017Entry Accepted: 01/03/2017Entry Last Modified: 05/30/2017Modify/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.