This article reviews recent advances in convex optimization algorithms for big data, which
aim to reduce the computational, storage, and communications bottlenecks. We provide an …

The paper presents a fully adaptive algorithm for monotone variational inequalities. In each
iteration the method uses two previous iterates for an approximation of the local Lipschitz …

We consider the minimization of a function G defined on R^N, which is the sum of a (not
necessarily convex) differentiable function and a (not necessarily differentiable) convex …

We study the minimization of a convex function f (X) over the set of n\times n positive semi-
definite matrices, but when the problem is recast as\min_U g (U):= f (UU^⊤), with …

A recent line of work has established uncoupled learning dynamics such that, when
employed by all players in a game, each player's regret after $ T $ repetitions grows …

Nonnegative matrix factorization (NMF) is a standard linear dimensionality reduction
technique for nonnegative data sets. In order to measure the discrepancy between the input …

The problem of Poisson denoising appears in various imaging applications, such as low-
light photography, medical imaging, and microscopy. In cases of high SNR, several …

We propose a new and low per-iteration complexity first-order primal-dual optimization
framework for a convex optimization template with broad applications. Our analysis relies on …

We study the smooth structure of convex functions by generalizing a powerful concept so-
called self-concordance introduced by Nesterov and Nemirovskii in the early 1990s to a …

The classical asymptotic theory for parametric M-estimators guarantees that, in the limit of
infinite sample size, the excess risk has a chi-square type distribution, even in the …