Applying bundle methods to the optimization of polyhedral functions: An applications-oriented development

Among practical methods for large-scale Nondifferentiable Optimization, bundle methods are widely recognized as playing a relevant role; despite their potential, however, they are not often used for maximization of polyhedral functions, that appear in many different context such as Lagrangean Duals and decomposition algorithms, since simpler-to-program but less efficient approaches like subgradient methods are preferred. The aim of this work is to provide an applications-oriented survey of the theory of bundle methods when applied to probles arising in continuous and combinatorial optimization, with an introduction to the several variants of Bundle approaches that can be built up by using a limited set of basic concepts and tools.