Incremental gradient, subgradient, and proximal methods for convex optimization: A survey
Page 100 4 Incremental Gradient, Subgradient, and Proximal Methods for Convex Optimization …

We consider the minimization of a sum i= 1^ mf_i (x) consisting of a large number of convex
component functions fi. For this problem, incremental methods consisting of gradient or …

The last few years have seen the advent of a new generation of bundle methods, capable to
handle inexact oracles, polluted by “noise”. Proving convergence of a bundle method is …

Joint chance constrained problems give rise to many algorithmic challenges. Even in the
convex case, ie, when an appropriate transformation of the probabilistic constraint is a …

In this paper, we study the influence of noise on subgradient methods for convex
constrained optimization. The noise may be due to various sources, and is manifested in …

In the standard classification problems, the objective is to categorize points into different
classes. Multiple instance learning (MIL), instead, is aimed at classifying bags of points …

For problems when decisions are taken prior to observing the realization of underlying
random events, probabilistic constraints are an important modeling tool if reliability is a …

We present an asynchronous bundle-trust-region algorithm within the context of Lagrangian
dual decomposition for stochastic mixed-integer programs. The approach solves the …

We review the basic ideas underlying the vast family of algorithms for nonsmooth convex
optimization known as “bundle methods”. In a nutshell, these approaches are based on …

An important field of application of non-smooth optimization refers to decomposition of large-
scale or complex problems by Lagrangian duality. In this setting, the dual problem consists …