## 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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Author: Matthias Ehrgott, Margaret M. Wiecek urn:nbn:de:hbz:386-kluedo-4737 Report in Wirtschaftsmathematik (WIMA Report) (30) Preprint English 1999 1999 Technische Universität Kaiserslautern 2000/04/03 Lagrangian Functions; Multiple Objective Programs ; Pareto Points ; Saddle Points Fachbereich Mathematik 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik 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 Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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