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Saddle Points and Pareto Points in Multiple Objective Programming

  • In this paper relationships between Pareto points and saddle points in multiple objective programming are investigated. Convex and nonconvex problems are considered and the equivalence between Pareto points and saddle points is proved in both cases. The results are based on scalarizations of multiple objective programs and related linear and augmented Lagrangian functions. Partitions of the index sets of objectives and constranints are introduced to reduce the size of the problems. The relevance of the results in the context of decision making is also discussed.

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Metadaten
Author:Matthias Ehrgott, Margaret M. Wiecek
URN:urn:nbn:de:hbz:386-kluedo-4737
Series (Serial Number):Report in Wirtschaftsmathematik (WIMA Report) (30)
Document Type:Preprint
Language of publication:English
Year of Completion:1999
Year of first Publication:1999
Publishing Institution:Technische Universität Kaiserslautern
Date of the Publication (Server):2000/04/03
Tag:Lagrangian Functions; Multiple Objective Programs; Pareto Points; Saddle Points
Faculties / Organisational entities:Kaiserslautern - Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
MSC-Classification (mathematics):90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C26 Nonconvex programming, global optimization
90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C29 Multi-objective and goal programming
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011