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Convergence of the Exponentiated Gradient Method with Armijo Line Search
Yen-Huan Li, Volkan Cevher
Consider the problem of minimizing a convex differentiable function on the probability simplex, spectrahedron, or set of quantum density matrices. We prove that the exponentiated g…
On the linear convergence of the stochastic gradient method with constant step-size
Volkan Cevher, Bang Cong Vu
The strong growth condition (SGC) is known to be a sufficient condition for linear convergence of the stochastic gradient method using a constant step-size (SGM-CS). In this pa…
Smooth Primal-Dual Coordinate Descent Algorithms for Nonsmooth Convex Optimization
Ahmet Alacaoglu, Quoc Tran-Dinh, Olivier Fercoq +1
We propose a new randomized coordinate descent method for a convex optimization template with broad applications. Our analysis relies on a novel combination of four ideas applied t…
Smoothing technique for nonsmooth composite minimization with linear operator
Quang Van Nguyen, Olivier Fercoq, Volkan Cevher
We introduce and analyze an algorithm for the minimization of convex functions that are the sum of differentiable terms and proximable terms composed with linear operators. The met…
A General Convergence Result for the Exponentiated Gradient Method
Yen-Huan Li, Volkan Cevher
The batch exponentiated gradient (EG) method provides a principled approach to convex smooth minimization on the probability simplex or the space of quantum density matrices. Howev…
Sketchy Decisions: Convex Low-Rank Matrix Optimization with Optimal Storage
Alp Yurtsever, Madeleine Udell, Joel A. Tropp +1
This paper concerns a fundamental class of convex matrix optimization problems. It presents the first algorithm that uses optimal storage and provably computes a low-rank approxima…
Stochastic Three-Composite Convex Minimization
Alp Yurtsever, Bang Cong Vu, Volkan Cevher
We propose a stochastic optimization method for the minimization of the sum of three convex functions, one of which has Lipschitz continuous gradient as well as restricted strong c…