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Duality theory in multiobjective programming. (English) Zbl 0378.90100

MSC:
90C99Mathematical programming
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References:
[1] Kuhn, H. W., andTucker, A. W.,Nonlinear Programming, pp. 416-427, Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, Berkeley, California, 1950.
[2] Da Cunha, N. O., andPolak, E.,Constrained Minimization under Vector-Valued Criteria in Finite Dimensional Spaces, Journal of Mathematical Analysis and Applications, Vol. 19, pp. 103-124, 1967. · Zbl 0154.44801 · doi:10.1016/0022-247X(67)90025-X
[3] Zadeh, L. A.,Optimality and Non-Scalar-Valued Performance Criteria, IEEE Transactions on Automatic Control, Vol. AC-8, pp. 59-60, 1967.
[4] Arrow, K. J., Hurwicz, L., andUzawa, H.,Studies in Linear and Nonlinear Programming, Stanford University Press, Stanford, California, 1958. · Zbl 0091.16002
[5] Yu, P. L.,Cone Convexity, Cone Extreme Points, and Nondominated Solutions in Decision Problems with Multiobjectives, Journal of Optimization Theory and Applications, Vol. 14, pp. 319-377, 1974. · Zbl 0268.90057 · doi:10.1007/BF00932614
[6] Luenberger, D. G.,Optimization by Vector Space Methods, John Wiley and Sons, New York, New York, 1969. · Zbl 0176.12701
[7] Geoffrion, A. M.,Proper Efficiency and the Theory of Vector Maximization, Journal of Mathematical Analysis and Applications, Vol. 22, pp. 618-630, 1968. · Zbl 0181.22806 · doi:10.1016/0022-247X(68)90201-1