Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/288330 
Year of Publication: 
2020
Citation: 
[Journal:] Journal of Global Optimization [ISSN:] 1573-2916 [Volume:] 80 [Issue:] 1 [Publisher:] Springer US [Place:] New York, NY [Year:] 2020 [Pages:] 63-86
Publisher: 
Springer US, New York, NY
Abstract: 
An important aspect of optimization algorithms, for instance evolutionary algorithms, are termination criteria that measure the proximity of the found solution to the optimal solution set. A frequently used approach is the numerical verification of necessary optimality conditions such as the Karush–Kuhn–Tucker (KKT) conditions. In this paper, we present a proximity measure which characterizes the violation of the KKT conditions. It can be computed easily and is continuous in every efficient solution. Hence, it can be used as an indicator for the proximity of a certain point to the set of efficient (Edgeworth-Pareto-minimal) solutions and is well suited for algorithmic use due to its continuity properties. This is especially useful within evolutionary algorithms for candidate selection and termination, which we also illustrate numerically for some test problems.
Subjects: 
Multiobjective optimization
KKT approximation
Proximity measure
JEL: 
C26
C29
C46
C59
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Article
Document Version: 
Published Version

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