article

On the completeness and constructiveness of parametric characterizations to vector optimization problems

Author:

A. P. WierzbickiAuthors Info & Claims

OR Spectrum, Volume 8, Issue 2

Pages 73 - 87

https://doi.org/10.1007/BF01719738

Published: 01 June 1986 Publication History

Abstract

Motivated by recent reviews of characterizations of optimal solutions to vector optimization problems and by applications to decision support systems, this paper presents a methodological approach to comparing such characterizations. After specifying attributes of constructiveness, alternative classes of characterizations are reviewed. Characterization theorems are quoted or presented in more detail in cases that supplement those given in recent reviews. One of alternative classes of characterizations -- by aspiration levels and order-consistent achievement functions -- is discussed in more detail. An impossibility theorem of complete and robustly computable characterization of efficient (as opposed to weakly or properly efficient) solutions to vector optimization problems is presented.

Angeregt durch neuere Übersichten der Charakterisierung von optimalen Lösungen von Vektoroptimierungsproblemen und durch Anwendungen auf Entscheidungsunterstützungssysteme wird in diesem Beitrag ein methodischer Ansatz zum Vergleich solcher Charakterisierungen dargestellt. Nach der Spezifizierung von Attributen der Konstruktivität werden alternative Klassen von Charakterisierungen betrachtet. Charakterisierungstheoreme werden entweder zitiert oder, in Ergänzung neuerer Übersichten, dargestellt. Eine der alternativen Klassen der Charakterisierungen wird näher diskutiert. Ein Unmöglichkeitstheorem einer vollständigen und robust berechenbaren Charakterisierung von effizienten (im Gegensatz zu schwach oder streng effizienten) Lösungen der Vektoroptimierungsprobleme wird dargelegt.

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On the completeness and constructiveness of parametric characterizations to vector optimization problems
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cover image OR Spectrum

OR Spectrum Volume 8, Issue 2

June 1986

71 pages

ISSN:0171-6468

Issue’s Table of Contents

Copyright © Copyright © 1986 Springer-Verlag.

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 01 June 1986

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Cited By

Helfrich SPrinz KRuzika S(2024)The Weighted p-Norm Weight Set Decomposition for Multiobjective Discrete Optimization ProblemsJournal of Optimization Theory and Applications10.1007/s10957-024-02481-8202:3(1187-1216)Online publication date: 1-Sep-2024
https://dl.acm.org/doi/10.1007/s10957-024-02481-8
Kashansky VAgha Hossein Kashani SZhuge HGarcia-Blas JMarozzo F(2023)Intelligent and Sustainable Transportation through Multi-Objective Model for the Logistic Route-Order Dispatching SystemProceedings of the 2023 ACM Conference on Information Technology for Social Good10.1145/3582515.3609578(530-536)Online publication date: 6-Sep-2023
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Guo FJiao L(2023)A new scheme for approximating the weakly efficient solution set of vector rational optimization problemsJournal of Global Optimization10.1007/s10898-023-01287-886:4(905-930)Online publication date: 2-May-2023
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