2014/07/28 by Kimon Fountoulakis, Fountoulakis, Kimon, Rachael Tappenden +1 · 2 citations
Computer Science · Engineering · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques #Stochastic Gradient Optimization Techniques #math.OC
paper · pdf · doi:10.48550/arxiv.1407.7573
23 pages, 6 figures
openalex publication_date 2014/07/28 · arxiv created 2015/05/08 · arxiv updated 2015/05/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we present a novel randomized block coordinate descent method for the minimization of a convex composite objective function. The method uses (approximate) partial second-order (curvature) information, so that the algorithm performance is more robust when applied to highly nonseparable or ill conditioned problems. We call the method Robust Coordinate Descent (RCD). At each iteration of RCD, a block of coordinates is sampled randomly, a quadratic model is formed about that block and the model is minimized approximately/inexactly to determine the search direction. An inexpensive line search is then employed to ensure a monotonic decrease in the objective function and acceptance of large step sizes. We prove global convergence of the RCD algorithm, and we also present several results on the local convergence of RCD for strongly convex functions. Finally, we present numerical results on large-scale problems to demonstrate the practical performance of the method.