Abstract
The properness of the efficient solution of the optimal problem with multicriteria has been independently defined by Kuhn and Tucker, Geoffrion, and Klinger. A theorem of Geoffrion describes the relation between Geoffrion's and Kuhn and Tucker's properness. In this paper, the dual part of the theorem is given, and some geometric approach is applied to derive the optimal conditions of proper efficient solutions and improper efficient solutions.
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Communicated by G. Leitmann
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Tamura, K., Arai, S. On proper and improper efficient solutions of optimal problems with multicriteria. J Optim Theory Appl 38, 191–205 (1982). https://doi.org/10.1007/BF00934082
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DOI: https://doi.org/10.1007/BF00934082