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Lagrange Multipliers and saddle points in multiobjective programming
Authors:Z F Li  S Y Wang
Institution:(1) Mathematics Department, University of Inner Mongolia, Hohhot, Inner Mongolia, China;(2) Institute of Systems Science, Academic Sinica, Beijing, China
Abstract:In this paper, we present several conditions for the existence of a Lagrange multiplier or a weak saddle point in multiobjective optimization. Relations between a Lagrange multiplier and a weak saddle point are established. A sufficient condition is also given for the equivalence of the Benson proper efficiency and the Borwein proper efficiency.This research was supported by NSFC under Grant No. 78900011 and by BMADIS. The authors are grateful to two referees for supplying valuable comments and pointing out detailed corrections to the draft paper. The authors also wish to thank Dr. P. L. Yu for valuable comments and suggestions.The revised version of this paper was completed while the second author visited the Faculty of Technical Mathematics and Informatics, Delft University of Technology, Delft, The Netherlands.
Keywords:Multiobjective programming  Lagrange multipliers  weak saddle points
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