A large number of imaging problems reduce to the optimization of a cost function, with
typical structural properties. The aim of this paper is to describe the state of the art in …

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 …

Just as in its 1st edition, this book starts with illustrations of the ubiquitous character of
optimization, and describes numerical algorithms in a tutorial way. It covers fundamental …

We investigate the behavior of quasi-Newton algorithms applied to minimize a nonsmooth
function f, not necessarily convex. We introduce an inexact line search that generates a …

The problem of finding a zero point of a maximal monotone operator plays a central role in
modeling many application problems arising from various fields, and the proximal point …

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 …

Polynomial extremal problems (PEP) constitute one of the most important subclasses of
nonlinear programming models. Their distinctive feature is that an objective function and …

This paper concerns with convergence properties of the classical proximal point algorithm
for finding zeroes of maximal monotone operators in an infinite-dimensional Hilbert space. It …

When computing the infimal convolution of a convex function f with the squared norm, the so-
called Moreau--Yosida regularization of f is obtained. Among other things, this function has a …

We propose a variable metric forward–backward splitting algorithm and prove its
convergence in real Hilbert spaces. We then use this framework to derive primal-dual …