Multiple instance learning (MIL) is a form of weakly supervised learning where training
instances are arranged in sets, called bags, and a label is provided for the entire bag. This …

Nonsmooth nonconvex optimization problems broadly emerge in machine learning and
business decision making, whereas two core challenges impede the development of …

Nonconvex optimization arises in many areas of computational science and engineering.
However, most nonconvex optimization algorithms are only known to have local …

Proximal bundle methods have been shown to be highly successful optimization methods
for unconstrained convex problems with discontinuous first derivatives. This naturally leads …

We present a framework for analyzing convergence and local rates of convergence of a
class of descent algorithms, assuming the objective function is weakly convex. The …

The proximal point map** is the basis of many optimization techniques for convex
functions. By means of variational analysis, the concept of proximal map** was recently …

We introduce a proximal bundle method for the numerical minimization of a nonsmooth
difference-of-convex (DC) function. Exploiting some classic ideas coming from cutting-plane …

We face a binary multiple instance learning (MIL) problem, whose objective is to
discriminate between two kinds of point sets: positive and negative. In the MIL terminology …

We present a bundle algorithm for multiple-instance classification and ranking. These
frameworks yield improved models on many problems possessing special structure. Multiple …

The aim of this paper is to introduce a new proximal double bundle method for
unconstrained nonsmooth optimization, where the objective function is presented as a …