On mixed integer nonsmooth optimization

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

doi:10.1007/978-3-030-34910-3_16

On mixed integer nonsmooth optimization

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

Tutkimustuotos: Artikkeli kirjassa/raportissa/konferenssijulkaisussa › Luku › Tieteellinen › vertaisarvioitu

1 Sitaatiot (Scopus)

62 Lataukset (Pure)

Abstrakti

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.

Alkuperäiskieli	Englanti
Otsikko	Numerical Nonsmooth Optimization
Alaotsikko	State of the Art Algorithms
Toimittajat	Adil M. Bagirov, Manlio Gaudioso, Napsu Karmitsa, Marko M. Mäkelä, Sona Taheri
Kustantaja	Springer, Cham
Sivut	549–578
Sivumäärä	30
ISBN (elektroninen)	978-3-030-34910-3
ISBN (painettu)	978-3-030-34909-7
DOI - pysyväislinkit	https://doi.org/10.1007/978-3-030-34910-3_16
Tila	Julkaistu - 2020
OKM-julkaisutyyppi	A3 Kirjan osa tai toinen tutkimuskirja

Pääsy asiakirjaan

10.1007/978-3-030-34910-3_16

2020-ChapterMINSO_EWMfinal-VPE-TW-MMMHyväksytty kirjoittajan käsikirjoitus, 202 KBLisenssi: Publisher rights policy

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title = "On mixed integer nonsmooth optimization",

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.",

author = "Ville-Pekka Eronen and Tapio Westerlund and M{\"a}kel{\"a}, {Marko M.}",

note = "ast Bara TY som affiliering i boken, men det h{\"o}r nog till {\AA}A. [Har kollat med AF 25.6.2020. LN] author's version of the accepted, peer-reviewed manuscript twelve months after publication Har kontaktat [email protected] den 26.6.2020 LN Tapio svarade att han inte f{\aa}tt filen {\"a}nnu. Han levererar s{\aa} fort han f{\aa}tt den. Linda validerade s{\aa} att den kommer {\"o}ver till Pure. Fulltexten b{\"o}r l{\"a}ggas till f{\"o}re rapporteringen.",

year = "2020",

doi = "10.1007/978-3-030-34910-3_16",

language = "English",

isbn = "978-3-030-34909-7",

pages = "549–578",

editor = "Bagirov, {Adil M.} and Manlio Gaudioso and Napsu Karmitsa and M{\"a}kel{\"a}, {Marko M.} and Sona Taheri",

booktitle = "Numerical Nonsmooth Optimization",

publisher = "Springer, Cham",

}

On mixed integer nonsmooth optimization. / Eronen, Ville-Pekka; Westerlund, Tapio; Mäkelä, Marko M.
Numerical Nonsmooth Optimization: State of the Art Algorithms. toim. / Adil M. Bagirov; Manlio Gaudioso; Napsu Karmitsa; Marko M. Mäkelä; Sona Taheri. Springer, Cham, 2020. s. 549–578.

Tutkimustuotos: Artikkeli kirjassa/raportissa/konferenssijulkaisussa › Luku › Tieteellinen › vertaisarvioitu

TY - CHAP

T1 - On mixed integer nonsmooth optimization

AU - Eronen, Ville-Pekka

AU - Westerlund, Tapio

AU - Mäkelä, Marko M.

N1 - ast Bara TY som affiliering i boken, men det hör nog till ÅA. [Har kollat med AF 25.6.2020. LN] author's version of the accepted, peer-reviewed manuscript twelve months after publication Har kontaktat [email protected] den 26.6.2020 LN Tapio svarade att han inte fått filen ännu. Han levererar så fort han fått den. Linda validerade så att den kommer över till Pure. Fulltexten bör läggas till före rapporteringen.

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

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M3 - Chapter

SN - 978-3-030-34909-7

SP - 549

EP - 578

BT - Numerical Nonsmooth Optimization

A2 - Bagirov, Adil M.

A2 - Gaudioso, Manlio

A2 - Karmitsa, Napsu

A2 - Mäkelä, Marko M.

A2 - Taheri, Sona

PB - Springer, Cham

ER -

On mixed integer nonsmooth optimization

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