Primal–dual accelerated gradient methods with small-dimensional relaxation oracle

Intermediate Gradient Methods for Smooth Convex Problems with Inexact Oracle

Between the robust but slow (primal or dual) gradient methods and the fast but sensitive to errors fast gradient methods, our goal in this paper is to develop first-order methods for smooth convex problems with intermediate speed and intermediate sensitivity to errors. We develop a general family of first-order methods, the Intermediate Gradient Method (IGM), based on two sequences of coefficie...

Accelerated Proximal Gradient Methods for Nonconvex Programming

Nonconvex and nonsmooth problems have recently received considerable attention in signal/image processing, statistics and machine learning. However, solving the nonconvex and nonsmooth optimization problems remains a big challenge. Accelerated proximal gradient (APG) is an excellent method for convex programming. However, it is still unknown whether the usual APG can ensure the convergence to a...

Accelerated Proximal Gradient Methods for Nonconvex Programming

Distributed Accelerated Proximal Coordinate Gradient Methods

We develop a general accelerated proximal coordinate descent algorithm in distributed settings (DisAPCG) for the optimization problem that minimizes the sum of two convex functions: the first part f is smooth with a gradient oracle, and the other one Ψ is separable with respect to blocks of coordinate and has a simple known structure (e.g., L1 norm). Our algorithm gets new accelerated convergen...

Better Mini-Batch Algorithms via Accelerated Gradient Methods

Mini-batch algorithms have been proposed as a way to speed-up stochastic convex optimization problems. We study how such algorithms can be improved using accelerated gradient methods. We provide a novel analysis, which shows how standard gradient methods may sometimes be insufficient to obtain a significant speed-up and propose a novel accelerated gradient algorithm, which deals with this defic...