Methods for Non-smooth Non-convex Optimization

Wim Stefanus Ackooij and Welington Luis de Oliveira
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Wim Stefanus Ackooij: Électricité de France (EDF R&D)
Welington Luis de Oliveira: Mines Paris - PSL

Chapter Chapter 14 in Methods of Nonsmooth Optimization in Stochastic Programming, 2025, pp 429-453 from Springer

Abstract: Abstract This chapter deals with the task of minimizing a class of locally Lipschitz functions over closed sets. The focus is given to local-solution methods for structured non-smooth and non-convex problems. Structures of interest include Difference-of-Convex (DC) and difference of Convex and weakly Convex (CwC) optimization problems. The chapter starts by revisiting the generalized Frank-Wolfe method, passing through the DC algorithm to more sophisticated bundle methods for problems whose objective and non-linear constraint can be expressed as CwC functions.

Keywords: Non-smooth optimization; Difference-of-convex programming; Difference of convex-and-weakly-convex methods (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/978-3-031-84837-7_14

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