The relationship between multi-objective robustness concepts and set-valued optimization

In this paper, we discuss the connection between concepts of robustness for multi-objective optimization problems and set order relations. We extend some of the existing concepts to general spaces and cones using set relations. Furthermore, we derive new concepts of robustness for multi-objective op...

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Published in:Fixed point theory and applications (Hindawi Publishing Corporation) Vol. 2014; no. 1; pp. 1 - 20
Main Authors: Ide, Jonas, Köbis, Elisabeth, Kuroiwa, Daishi, Schöbel, Anita, Tammer, Christiane
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 31.03.2014
Subjects:
Algorithms
Analysis
Applications of Mathematics
Cones
Differential Geometry
Joints
Mathematical and Computational Biology
Mathematics
Mathematics and Statistics
Optimization
Robustness
Topology
Variational Analysis and Fixed Point Theory
vectorization
scalarization
set-valued optimization
multi-objective optimization
robust optimization
ISSN:1687-1820, 1687-1812
Online Access:Get full text
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Abstract In this paper, we discuss the connection between concepts of robustness for multi-objective optimization problems and set order relations. We extend some of the existing concepts to general spaces and cones using set relations. Furthermore, we derive new concepts of robustness for multi-objective optimization problems. We point out that robust multi-objective optimization can be interpreted as an application of set-valued optimization. Furthermore, we develop new algorithms for solving uncertain multi-objective optimization problems. These algorithms can be used in order to solve a special class of set-valued optimization problems.
AbstractList In this paper, we discuss the connection between concepts of robustness for multi-objective optimization problems and set order relations. We extend some of the existing concepts to general spaces and cones using set relations. Furthermore, we derive new concepts of robustness for multi-objective optimization problems. We point out that robust multi-objective optimization can be interpreted as an application of set-valued optimization. Furthermore, we develop new algorithms for solving uncertain multi-objective optimization problems. These algorithms can be used in order to solve a special class of set-valued optimization problems.
Author Kuroiwa, Daishi
Schöbel, Anita
Ide, Jonas
Tammer, Christiane
Köbis, Elisabeth
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  organization: Martin-Luther-University Halle-Wittenberg
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10.1007/978-1-4757-2620-6
10.1007/BFb0056855
10.1007/978-3-642-19754-3_15
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Copyright Ide et al.; licensee Springer. 2014. This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited.
Copyright_xml – notice: Ide et al.; licensee Springer. 2014. This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited.
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Keywords vectorization
scalarization
set-valued optimization
multi-objective optimization
robust optimization
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SubjectTerms Algorithms
Analysis
Applications of Mathematics
Cones
Differential Geometry
Joints
Mathematical and Computational Biology
Mathematics
Mathematics and Statistics
Optimization
Robustness
Topology
Variational Analysis and Fixed Point Theory
Title The relationship between multi-objective robustness concepts and set-valued optimization
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