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

This book is the first easy-to-read text on nonsmooth optimization (NSO, not necessarily
differentiable optimization). Solving these kinds of problems plays a critical role in many …

We consider optimization problems with objective and constraint functions that may be
nonconvex and nonsmooth. Problems of this type arise in important applications, many …

A line search algorithm for minimizing nonconvex and/or nonsmooth objective functions is
presented. The algorithm is a hybrid between a standard Broyden–Fletcher–Goldfarb …

The goal of this paper is to investigate an approach for derivative-free optimization that has
not received sufficient attention in the literature and is yet one of the simplest to implement …

We develop an algorithm for minimax problems that arise in robust optimization in the
absence of objective function derivatives. The algorithm utilizes an extension of methods for …

We present an efficient descent method for unconstrained, locally Lipschitz multiobjective
optimization problems. The method is realized by combining a theoretical result regarding …

We consider a degenerate nonsmooth and nonconvex optimization problem for which the
standard constraint qualification such as the generalized Mangasarian--Fromovitz constraint …

Associating distinct groups of objects (clusters) with contiguous regions of high probability
density (high-density clusters), is central to many statistical and machine learning …

Single image dehazing has always been a challenging problem in the field of computer
vision. Traditional image defogging methods use manual features. With the development of …