Limited Memory Bundle Method and Its Variations for Large-Scale Nonsmooth Optimization

Napsu Karmitsa ()
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Napsu Karmitsa: Department of Mathematics and Statistics, University of Turku

Chapter Chapter 5 in Numerical Nonsmooth Optimization, 2020, pp 167-199 from Springer

Abstract: Abstract There exist a vast variety of practical problems involving nonsmooth functions with large dimensions and nonconvex characteristics. Nevertheless, most nonsmooth solution methods have been designed to solve only small- or medium scale problems and they are heavily based on the convexity of the problem. In this chapter we describe three numerical methods for solving large-scale nonconvex NSO problems. Namely, the limited memory bundle algorithm (LMBM), the diagonal bundle method (D-Bundle), and the splitting metrics diagonal bundle method (SMDB). We also recall the convergence properties of these algorithms. To demonstrate the usability of the methods in large-scale settings, numerical experiments have been made using academic NSO problems with up to million variables.

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-34910-3_5

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DOI: 10.1007/978-3-030-34910-3_5

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