This article reviews the gradient sampling methodology for solving nonsmooth, nonconvex
optimization problems. We state an intuitively straightforward gradient sampling algorithm …

In view of the minimization of a nonsmooth nonconvex function f, we prove an abstract
convergence result for descent methods satisfying a sufficient-decrease assumption, and …

In this paper, we study the Kurdyka–Łojasiewicz (KL) exponent, an important quantity for
analyzing the convergence rate of first-order methods. Specifically, we develop various …

Variational analysis has been recognized as a fruitful area in mathematics that on the one
hand deals with the study of optimization and equilibrium problems and on the other hand …

We have already seen that linear functions are always continuous. More generally, a
remarkable feature of convex functions on E is that they must be continuous on the interior of …

We study the convergence of the proximal algorithm applied to nonsmooth functions that
satisfy the Łjasiewicz inequality around their generalized critical points. Typical examples of …

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 …

We establish the following result: If the graph of a lower semicontinuous real-extended-
valued function f:R^n→R∪{+∞\} admits a Whitney stratification (so in particular if f is a …

We present PANOC, a new algorithm for solving optimal control problems arising in
nonlinear model predictive control (NMPC). A usual approach to this type of problems is …

We propose\sf ZeroFPR, a nonmonotone linesearch algorithm for minimizing the sum of two
nonconvex functions, one of which is smooth and the other possibly nonsmooth.\sf ZeroFPR …