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

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	915-922
Number of pages	8
Journal	Optimization Letters
Volume	12
Issue number	4
DOIs	https://doi.org/10.1007/s11590-017-1164-3
Publication status	Published - 1 Jun 2018
Externally published	Yes

Keywords

Cones
Minimality
Proper minimality
Quasi interior
Vector duality

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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",

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

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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

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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

Abstract

Keywords

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