Constrained optimization using multiple objective programming

In practical applications of mathematical programming it is frequently observed that the decision maker prefers apparently suboptimal solutions. A natural explanation for this phenomenon is that the applied mathematical model was not sufficiently realistic and did not fully represent all the decisio...

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Veröffentlicht in:Journal of global optimization Jg. 37; H. 3; S. 325 - 355
Hauptverfasser: Klamroth, Kathrin, Jørgen, Tind
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Dordrecht Springer Nature B.V 01.03.2007
Schlagworte:
Applied mathematics
Approximation
Capital budgeting
Convergence
Decision making
Design
Design engineering
Genetic algorithms
Mathematical programming
Methods
Optimization
Optimization techniques
Studies
Violations
ISSN:0925-5001, 1573-2916
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Zusammenfassung:In practical applications of mathematical programming it is frequently observed that the decision maker prefers apparently suboptimal solutions. A natural explanation for this phenomenon is that the applied mathematical model was not sufficiently realistic and did not fully represent all the decision makers criteria and constraints. Since multicriteria optimization approaches are specifically designed to incorporate such complex preference structures, they gain more and more importance in application areas as, for example, engineering design and capital budgeting. The aim of this paper is to analyze optimization problems both from a constrained programming and a multicriteria programming perspective. It is shown that both formulations share important properties, and that many classical solution approaches have correspondences in the respective models. The analysis naturally leads to a discussion of the applicability of some recent approximation techniques for multicriteria programming problems for the approximation of optimal solutions and of Lagrange multipliers in convex constrained programming. Convergence results are proven for convex and nonconvex problems. [PUBLICATION ABSTRACT]
Bibliographie:SourceType-Scholarly Journals-1
ObjectType-Feature-1
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-006-9052-x