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

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

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.

Original language	English
Pages (from-to)	417-444
Number of pages	28
Journal	Mathematical Methods of Operations Research
Volume	65
Issue number	3
DOIs	https://doi.org/10.1007/s00186-006-0125-x
Publication status	Published - 1 Jun 2007
Externally published	Yes

Keywords

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

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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",

year = "2007",

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AU - Grad, Sorin Mihai

AU - Wanka, Gert

PY - 2007/6/1

Y1 - 2007/6/1

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

U2 - 10.1007/s00186-006-0125-x

DO - 10.1007/s00186-006-0125-x

M3 - Article

AN - SCOPUS:34249899662

SN - 1432-2994

VL - 65

SP - 417

EP - 444

JO - Mathematical Methods of Operations Research

JF - Mathematical Methods of Operations Research

IS - 3

ER -

A general approach for studying duality in multiobjective optimization

Abstract

Keywords

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