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

Research output: Chapter in Book/Conference proceeding › Chapter › Scientific › peer-review

1 Citation (Scopus)

59 Downloads (Pure)

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 language	English
Title of host publication	Numerical Nonsmooth Optimization
Subtitle of host publication	State of the Art Algorithms
Editors	Adil M. Bagirov, Manlio Gaudioso, Napsu Karmitsa, Marko M. Mäkelä, Sona Taheri
Publisher	Springer, Cham
Pages	549–578
Number of pages	30
ISBN (Electronic)	978-3-030-34910-3
ISBN (Print)	978-3-030-34909-7
DOIs	https://doi.org/10.1007/978-3-030-34910-3_16
Publication status	Published - 2020
MoE publication type	A3 Part of a book or another research book

Access to Document

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

2020-ChapterMINSO_EWMfinal-VPE-TW-MMMAccepted author manuscript, 202 KBLicence: Publisher rights policy

Cite this

@inbook{b1283956f1e04fc1b9aad3040fcc73c1,

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. ed. / Adil M. Bagirov; Manlio Gaudioso; Napsu Karmitsa; Marko M. Mäkelä; Sona Taheri. Springer, Cham, 2020. p. 549–578.

Research output: Chapter in Book/Conference proceeding › Chapter › Scientific › peer-review

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.

UR - http://www.scopus.com/inward/record.url?scp=85088473852&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-34910-3_16

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

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

Abstract

Access to Document

Other files and links

Fingerprint

Cite this