Many problems of recent interest in statistics and machine learning can be posed in the
framework of convex optimization. Due to the explosion in size and complexity of modern …

Recently, alternating direction method of multipliers (ADMM) attracts much attentions from
various fields and there are many variant versions tailored for different models. Moreover, its …

Starting from where a first course in convex optimization leaves off, this text presents a
unified analysis of first-order optimization methods–including parallel-distributed algorithms …

In this paper we consider solving saddle point problems using two variants of Gradient
Descent-Ascent algorithms, Extra-gradient (EG) and Optimistic Gradient Descent Ascent …

This monograph covers some recent advances in a range of acceleration techniques
frequently used in convex optimization. We first use quadratic optimization problems to …

This monograph is about a class of optimization algorithms called proximal algorithms. Much
like Newton's method is a standard tool for solving unconstrained smooth optimization …

The alternating direction method of multipliers (ADMM) is now widely used in many fields,
and its convergence was proved when two blocks of variables are alternatively updated. It is …

This tutorial paper presents the basic notation and results of monotone operators and
operator splitting methods, with a focus on convex optimization. A very wide variety of …

From its origins in the minimization of integral functionals, the notion of'variations' has
evolved greatly in connection with applications in optimization, equilibrium, and control. It …

For the problem of minimizing a lower semicontinuous proper convex function f on a Hilbert
space, the proximal point algorithm in exact form generates a sequence {z^k\} by taking …