Abstract
A new characterization is obtained for the existence of an efficient solution of a vector optimization problem in terms of associated scalar optimization problems. The consequences for linear vector optimization problems are derived as a special case, Applications to convex vector optimization problems are also discussed.
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Borwein, J. M., On the Existence of Pareto Efficient Points, Mathematics of Operations Research, Vol. 8, pp. 64–73, 1983.
Sawaragi, Y., Nakayama, H., and Tanino, T., Theory of Multiobjective Optimization, Academic Press, New York, New York, 1985.
Henig, M. I., Existence and Characterization of Efficient Decisions with Respect to Cones, Mathematical Programming, Vol. 23, pp. 111–116, 1982.
Bitran, G. R., and Magnanti, T. L., The Structure of Admissible Points with Respect to Cone Dominance, Journal of Optimization Theory and Applications, Vol. 29, pp. 573–614, 1979.
Ruiz-Canales, P., and Rufian-Lizana, A., A Characterization of Weakly Efficient Points, Mathematical Programming, Vol. 68, pp. 205–212, 1995.
Rockafellar, R. T., Convex Analysis, Princeton University Press, Princeton, New Jersey, 1970.
Hiriart-Urruty, J. B., and Lemarechal, C., Convex Analysis and Minimization Algorithms, Vol. 1, Springer Verlag, Berlin, Germany, 1993.
Deng, S., Characterizations of the Nonemptiness and Compactness of Solution Sets in Convex Vector Optimization, Journal of Optimization Theory and Applications, Vol. 96, pp. 123–131, 1998.
Cheng, G. Y. and Craven, B. D., Existence and Continuity of Solutions for Vector Optimization, Journal of Optimization Theory and Applications, Vol. 81, pp. 459–467, 1994.
Deng, S., On Approximate Solutions in Convex Vector Optimization, SIAM Journal on Control and Optimization, Vol. 35, pp. 2128–2136, 1997.
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Deng, S. On Efficient Solutions in Vector Optimization. Journal of Optimization Theory and Applications 96, 201–209 (1998). https://doi.org/10.1023/A:1022627520279
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DOI: https://doi.org/10.1023/A:1022627520279