Abstract
In this paper, we discuss the optimality conditions for vector optimization problems. Properties of efficient and weakly efficient solutions are studied, and some new necessary conditions are obtained. Most of them are related to the mapping properties of the derivative operatorf′(x) of the objective functionf. Almost all of our results are based on the methods of functional analysis and the theory of degree.
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Communicated by G. Leitmann
The authors would like to thank Professor Y. D. Hu, Deputy General Secretary of the Chinese Operations Research Society, for his help and directions. Also, the authors would like to thank Professors T. K. Sung and Y. J. Chang, Chairmen of the authors' present department, for their sincere concern and encouragement. Finally, the authors are grateful to Professor G. Leitmann for his valuable comments, suggestions, and his careful editing of an earlier version of this paper.
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Bu, Q.Y., Shen, H.R. Some properties of efficient solutions for vector optimization. J Optim Theory Appl 46, 255–263 (1985). https://doi.org/10.1007/BF00939284
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DOI: https://doi.org/10.1007/BF00939284