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Benson, H. P.

On a domination property for vector maximization with respect to cones. (English) Zbl 0479.90075

J. Optimization Theory Appl. 39, 125-132 (1983).
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Cited in 1 Review
Cited in 14 Documents

MSC:

90C31 Sensitivity, stability, parametric optimization

Keywords:

maximization with respect to cones; domination property; efficient points; proper efficiency; nondominated points; sufficient domination condition; vector optimization
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Full Text: DOI

References:

[1] Stadler, W.,A Survey of Multicriteria Optimization or the Vector Maximum Problem, Part 1: 1776-1960, Journal of Optimization Theory and Applications, Vol. 29, pp. 1-52, 1979. · Zbl 0388.90001 · doi:10.1007/BF00932634
[2] Kuhn, H. W., andTucker, A. W.,Nonlinear Programming, Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, Edited by J. Neyman, University of California Press, Berkeley, California, 1950.
[3] 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
[4] Philip, J.,Algorithms for the Vector Maximization Problem, Mathematical Programming, Vol. 2, pp. 207-229, 1972. · Zbl 0288.90052 · doi:10.1007/BF01584543
[5] Evans, J. P., andSteuer, R. E.,A Revised Simplex Method for Linear Multiple Objective Programs, Mathematical Programming, Vol. 5, pp. 54-72, 1973. · Zbl 0281.90045 · doi:10.1007/BF01580111
[6] Zeleny, M.,Linear Multiobjective Programming, Springer-Verlag, Berlin, Germany, 1974. · Zbl 0325.90033
[7] 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
[8] Yu, P. L., andZeleny, M.,The Set of all Nondominated Solutions in Linear Cases and a Multicriteria Simplex Method, Journal of Mathematical Analysis and Applications, Vol. 49, pp. 430-468, 1975. · Zbl 0313.65047 · doi:10.1016/0022-247X(75)90189-4
[9] Borwein, J.,Proper Efficient Points for Maximizations with Respect to Cones, SIAM Journal on Control and Optimization, Vol. 15, pp. 57-63, 1977. · Zbl 0369.90096 · doi:10.1137/0315004
[10] Naccache, P. H.,Connectedness of the Set of Nondominated Outcomes in Multicriteria Optimization, Journal of Optimization Theory and Applications, Vol. 25, pp. 459-467, 1978. · Zbl 0363.90108 · doi:10.1007/BF00932907
[11] Benson, H. P.,An Improved Definition of Proper Efficiency for Vector Maximization with Respect to Cones, Journal of Mathematical Analysis and Applications, Vol. 71, pp. 232-241, 1979. · Zbl 0418.90081 · doi:10.1016/0022-247X(79)90226-9
[12] Bitran, G. R., andMagnanti, T. L.,The Structure of Admissible Points with Respect to Cone Dominance, Journal of Optimization Theory and Applications, Vol. 29, pp. 573-614, 1979. · Zbl 0389.52021 · doi:10.1007/BF00934453
[13] Henig, M. I.,Proper Efficiency with Respect to Cones, Journal of Optimization Theory and Applications, Vol. 36, pp. 387-407, 1982. · Zbl 0452.90073 · doi:10.1007/BF00934353
[14] Bragard, L., andVangeld?re, J.,Points Efficaces en Programmation ? Objectifs Multiples, Bulletin de la Soci?t? Royale des Sciences de Li?ge, Vol. 46, pp. 27-41, 1977.
[15] Rockafellar, R. T.,Convex Analysis, Princeton University Press, Princeton, New Jersey, 1970. · Zbl 0193.18401
[16] Benson, H. P.,Efficiency and Proper Efficiency in Vector Maximization with Respect to Cones, Journal of Mathematical Analysis and Applications (to appear). · Zbl 0519.90080
[17] Isermann, H.,Proper Efficiency and the Linear Vector Maximum Problem, Operations Research, Vol. 15, pp. 189-191, 1974. · Zbl 0274.90024 · doi:10.1287/opre.22.1.189
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