On mixed integer nonsmooth optimization

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

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Sammanfattning

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.

OriginalspråkEngelska
Titel på gästpublikationNumerical Nonsmooth Optimization
Undertitel på gästpublikationState of the Art Algorithms
RedaktörerAdil M. Bagirov, Manlio Gaudioso, Napsu Karmitsa, Marko M. Mäkelä, Sona Taheri
FörlagSpringer, Cham
Sidor549–578
Antal sidor30
ISBN (elektroniskt)978-3-030-34910-3
ISBN (tryckt)978-3-030-34909-7
DOI
StatusPublicerad - 2020
MoE-publikationstypA3 Del av bok eller annan forskningsbok

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