Properly efficient and efficient solutions for vector maximization problems in euclidean space

J. W. Nieuwenhuis

doi:10.1016/0022-247X(81)90169-4

Properly efficient and efficient solutions for vector maximization problems in euclidean space

J. W. Nieuwenhuis^*

^*Corresponding author for this work

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Abstract

Recently Benson proposed a definition for extending Geoffrion's concept of proper efficiency to the vector maximization problem in which the domination cone K is any nontrivial, closed convex cone. We give an equivalent definition of his notion of proper efficiency. Our definition, by means of perturbation of the cone K, seems to offer another justification of Benson's choice above Borwein's extension of Geoffrion's concept. Our result enables one to prove some other theorems concerning properly efficient and efficient points. Among these is a connectedness result.

Original language	English
Pages (from-to)	311-317
Number of pages	7
Journal	Journal of Mathematical Analysis and Applications
Volume	84
Issue number	2
DOIs	https://doi.org/10.1016/0022-247X(81)90169-4
Publication status	Published - 1981

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Properly efficient and efficient solutions for vector maximization problems in euclidean spaceFinal publisher's version, 311 KBLicence: Elsevier

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title = "Properly efficient and efficient solutions for vector maximization problems in euclidean space",

abstract = "Recently Benson proposed a definition for extending Geoffrion's concept of proper efficiency to the vector maximization problem in which the domination cone K is any nontrivial, closed convex cone. We give an equivalent definition of his notion of proper efficiency. Our definition, by means of perturbation of the cone K, seems to offer another justification of Benson's choice above Borwein's extension of Geoffrion's concept. Our result enables one to prove some other theorems concerning properly efficient and efficient points. Among these is a connectedness result.",

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AU - Nieuwenhuis, J. W.

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AB - Recently Benson proposed a definition for extending Geoffrion's concept of proper efficiency to the vector maximization problem in which the domination cone K is any nontrivial, closed convex cone. We give an equivalent definition of his notion of proper efficiency. Our definition, by means of perturbation of the cone K, seems to offer another justification of Benson's choice above Borwein's extension of Geoffrion's concept. Our result enables one to prove some other theorems concerning properly efficient and efficient points. Among these is a connectedness result.

U2 - 10.1016/0022-247X(81)90169-4

DO - 10.1016/0022-247X(81)90169-4

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JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

Properly efficient and efficient solutions for vector maximization problems in euclidean space

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