Characterizations via linear scalarization of minimal and properly minimal elements

Sorin Mihai Grad

doi:10.1007/s11590-017-1164-3

Characterizations via linear scalarization of minimal and properly minimal elements

Sorin Mihai Grad

Fac. Math. of the TU

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

3 Citations (Scopus)

Résumé

In this note we provide sufficient conditions that guarantee representations via linear scalarization of different types of properly minimal elements of a given set by means of a new separation statement for closed convex cones. Moreover, we also give conditions that ensure the proper minimality (in different senses) of the minimal points with respect to a convex ordering cone of a set.

langue originale	Anglais
Pages (de - à)	915-922
Nombre de pages	8
journal	Optimization Letters
Volume	12
Numéro de publication	4
Les DOIs	https://doi.org/10.1007/s11590-017-1164-3
état	Publié - 1 juin 2018
Modification externe	Oui

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10.1007/s11590-017-1164-3

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title = "Characterizations via linear scalarization of minimal and properly minimal elements",

abstract = "In this note we provide sufficient conditions that guarantee representations via linear scalarization of different types of properly minimal elements of a given set by means of a new separation statement for closed convex cones. Moreover, we also give conditions that ensure the proper minimality (in different senses) of the minimal points with respect to a convex ordering cone of a set.",

keywords = "Cones, Minimality, Proper minimality, Quasi interior, Vector duality",

author = "Grad, \{Sorin Mihai\}",

note = "Publisher Copyright: {\textcopyright} 2017, Springer-Verlag GmbH Germany.",

year = "2018",

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doi = "10.1007/s11590-017-1164-3",

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T1 - Characterizations via linear scalarization of minimal and properly minimal elements

AU - Grad, Sorin Mihai

PY - 2018/6/1

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N2 - In this note we provide sufficient conditions that guarantee representations via linear scalarization of different types of properly minimal elements of a given set by means of a new separation statement for closed convex cones. Moreover, we also give conditions that ensure the proper minimality (in different senses) of the minimal points with respect to a convex ordering cone of a set.

AB - In this note we provide sufficient conditions that guarantee representations via linear scalarization of different types of properly minimal elements of a given set by means of a new separation statement for closed convex cones. Moreover, we also give conditions that ensure the proper minimality (in different senses) of the minimal points with respect to a convex ordering cone of a set.

KW - Cones

KW - Minimality

KW - Proper minimality

KW - Quasi interior

KW - Vector duality

U2 - 10.1007/s11590-017-1164-3

DO - 10.1007/s11590-017-1164-3

M3 - Article

AN - SCOPUS:85021246610

SN - 1862-4472

VL - 12

SP - 915

EP - 922

JO - Optimization Letters

JF - Optimization Letters

IS - 4

ER -

Characterizations via linear scalarization of minimal and properly minimal elements

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