On Optimization over the Efficient Set in Linear Multicriteria Programming

The efficient set of a linear multicriteria programming problem can be represented\nby a reverse convex constraint of the form g(z) ≤ 0, where g is a concave\nfunction. Consequently, the problem of optimizing some real function over the efficient\nset belongs to an important problem class of global...

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Bibliographic Details
Published in:Journal of optimization theory and applications Vol. 134; no. 3; pp. 433 - 443
Main Authors: 山本 芳嗣, Horst R., Thoai N.V., Yamamoto Yoshitsugu, Zenke D.
Format: Journal Article
Language:English
Published: New York, NY Springer Verlag 01.09.2007
Springer
Springer Nature B.V
Subjects:
Algorithms
Applied sciences
Construction
Euclidean space
Exact sciences and technology
Handling
Linear programming
Materials handling
Mathematical programming
Multiple criteria decision making
Operational research and scientific management
Operational research. Management science
Optimization
Optimization techniques
Programming
Studies
Optimization over the efficient set
Multicriteria analysis
Linear form
Global optimum
Linear programming
Multicriteria optimization
Minimum maximal flow problem
Convex programming
Optimization
Concave function
Global optimization
Real function
Minimax problem
Reverse convex constraint
Optimal flow
ISSN:0022-3239, 1573-2878
Online Access:Get full text
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Summary:The efficient set of a linear multicriteria programming problem can be represented\nby a reverse convex constraint of the form g(z) ≤ 0, where g is a concave\nfunction. Consequently, the problem of optimizing some real function over the efficient\nset belongs to an important problem class of global optimization called reverse\nconvex programming. Since the concave function used in the literature is only defined\non some set containing the feasible set of the underlying multicriteria programming\nproblem, most global optimization techniques for handling this kind of reverse convex\nconstraint cannot be applied. The main purpose of our article is to present a\nmethod for overcoming this disadvantage. We construct a concave function which is\nfinitely defined on the whole space and can be considered as an extension of the existing\nfunction. Different forms of the linear multicriteria programming problem are\ndiscussed, including the minimum maximal flow problem as an example. application/pdf
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-007-9219-8