A conic scalarization method in multi-objective optimization

This paper presents the conic scalarization method for scalarization of nonlinear multi-objective optimization problems. We introduce a special class of monotonically increasing sublinear scalarizing functions and show that the zero sublevel set of every function from this class is a convex closed a...

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Veröffentlicht in:Journal of global optimization Jg. 56; H. 2; S. 279 - 297
1. Verfasser: Kasimbeyli, Refail
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Boston Springer US 01.06.2013
Springer
Springer Nature B.V
Schlagworte:
Analysis
Augmentation
Computer Science
Conics
Decision making
Economic theory
Mathematical analysis
Mathematical functions
Mathematics
Mathematics and Statistics
Methods
Nonlinearity
Norms
Operations Research/Decision Theory
Optimization
Real Functions
Scalars
Studies
Vectors (mathematics)
Separable cone
Multi-objective optimization
Augmented dual cones
Sublinear scalarizing functions
Conic scalarization method
Proper efficiency
Cone separation theorem
ISSN:0925-5001, 1573-2916
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Zusammenfassung:This paper presents the conic scalarization method for scalarization of nonlinear multi-objective optimization problems. We introduce a special class of monotonically increasing sublinear scalarizing functions and show that the zero sublevel set of every function from this class is a convex closed and pointed cone which contains the negative ordering cone. We introduce the notion of a separable cone and show that two closed cones (one of them is separable) having only the vertex in common can be separated by a zero sublevel set of some function from this class. It is shown that the scalar optimization problem constructed by using these functions, enables to characterize the complete set of efficient and properly efficient solutions of multi-objective problems without convexity and boundedness conditions. By choosing a suitable scalarizing parameter set consisting of a weighting vector, an augmentation parameter, and a reference point, decision maker may guarantee a most preferred efficient or properly efficient solution.
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-011-9789-8