A general approach for studying duality in multiobjective optimization

Radu Ioan Boţ; Sorin Mihai Grad; Gert Wanka

doi:10.1007/s00186-006-0125-x

A general approach for studying duality in multiobjective optimization

Radu Ioan Boţ
, Sorin Mihai Grad
, Gert Wanka

Fac. Math. of the TU

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

Résumé

A general duality framework in convex multiobjective optimization is established using the scalarization with K-strongly increasing functions and the conjugate duality for composed convex cone-constrained optimization problems. Other scalarizations used in the literature arise as particular cases and the general duality is specialized for some of them, namely linear scalarization, maximum (-linear) scalarization, set scalarization, (semi)norm scalarization and quadratic scalarization.

langue originale	Anglais
Pages (de - à)	417-444
Nombre de pages	28
journal	Mathematical Methods of Operations Research
Volume	65
Numéro de publication	3
Les DOIs	https://doi.org/10.1007/s00186-006-0125-x
état	Publié - 1 juin 2007
Modification externe	Oui

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10.1007/s00186-006-0125-x

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title = "A general approach for studying duality in multiobjective optimization",

abstract = "A general duality framework in convex multiobjective optimization is established using the scalarization with K-strongly increasing functions and the conjugate duality for composed convex cone-constrained optimization problems. Other scalarizations used in the literature arise as particular cases and the general duality is specialized for some of them, namely linear scalarization, maximum (-linear) scalarization, set scalarization, (semi)norm scalarization and quadratic scalarization.",

keywords = "Composed convex optimization problems, Efficient solutions (properly, weakly), Fenchel-Lagrange duality, Multiobjective duality",

author = "Bo{\c t}, \{Radu Ioan\} and Grad, \{Sorin Mihai\} and Gert Wanka",

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N2 - A general duality framework in convex multiobjective optimization is established using the scalarization with K-strongly increasing functions and the conjugate duality for composed convex cone-constrained optimization problems. Other scalarizations used in the literature arise as particular cases and the general duality is specialized for some of them, namely linear scalarization, maximum (-linear) scalarization, set scalarization, (semi)norm scalarization and quadratic scalarization.

AB - A general duality framework in convex multiobjective optimization is established using the scalarization with K-strongly increasing functions and the conjugate duality for composed convex cone-constrained optimization problems. Other scalarizations used in the literature arise as particular cases and the general duality is specialized for some of them, namely linear scalarization, maximum (-linear) scalarization, set scalarization, (semi)norm scalarization and quadratic scalarization.

KW - Composed convex optimization problems

KW - Efficient solutions (properly, weakly)

KW - Fenchel-Lagrange duality

KW - Multiobjective duality

UR - https://www.scopus.com/pages/publications/34249899662

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DO - 10.1007/s00186-006-0125-x

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JO - Mathematical Methods of Operations Research

JF - Mathematical Methods of Operations Research

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ER -

A general approach for studying duality in multiobjective optimization

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