On mixed integer nonsmooth optimization

Ville-Pekka Eronen, Tapio Westerlund, Marko M. Mäkelä

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Abstract

In this chapter we review some deterministic solution methods for convex mixed integer nonsmooth optimization problems. The methods are branch and bound, outer approximation, extended cutting plane, extended supporting hyperplane and extended level bundle method. Nonsmoothness is taken into account by using Clarke subgradients as a substitute for the classical gradient. Ideas for convergence proofs are given as well as references where the details can be found. We also consider how some algorithms can be modified in order to solve nonconvex problems including f∘-pseudoconvex functions or even f∘-quasiconvex constraints.

Original languageEnglish
Title of host publicationNumerical Nonsmooth Optimization
Subtitle of host publicationState of the Art Algorithms
EditorsAdil M. Bagirov, Manlio Gaudioso, Napsu Karmitsa, Marko M. Mäkelä, Sona Taheri
PublisherSpringer, Cham
Pages549–578
Number of pages30
ISBN (Electronic)978-3-030-34910-3
ISBN (Print)978-3-030-34909-7
DOIs
Publication statusPublished - 2020
MoE publication typeA3 Part of a book or another research book

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