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Proper efficiency with respect to cones. (English) Zbl 0452.90073

MSC:
90C31Sensitivity, stability, parametric optimization
References:
[1]Cochrane, J. L., andZeleny, M., Editors,Multiple Criteria Decision-Making, University of South Carolina Press, Columbia, South Carolina, 1973.
[2]Bitran, G., andMagnanti, T.,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
[3]Kuhn, H. W., andTucker, A. W.,Nonlinear Programming, Second Berkeley Symposium on Mathematical Statistics and Probability, Edited by J. Neyman, University of California Press, Berkeley, California, 1951.
[4]Geoffrion, A. M.,Proper Efficiency and the Theory of Vector Maximization, Journal of Mathematical Analysis and Applications, Vol. 22, pp. 613-630, 1968. · Zbl 0181.22806 · doi:10.1016/0022-247X(68)90201-1
[5]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
[6]Benson, B.,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
[7]Benson, H., andMorin, T.,The Vector Maximization Problems: Proper Efficiency and Stability, SIAM Journal on Applied Mathematics, Vol. 32, pp. 64-72, 1977. · Zbl 0357.90059 · doi:10.1137/0132004
[8]Yu, P. L.,Cone Convexity, Cone Extreme Points, and Nondominated Solutions in Decision Problems with Multi-Objectives, Journal of Optimization Theory and Applications, Vol. 14, pp. 319-377, 1974. · Zbl 0268.90057 · doi:10.1007/BF00932614
[9]Rockafellar, R. T.,Convex Analysis, Princeton University Press, Princeton, New Jersey, 1970.
[10]Henig, M. I.,A Cone Separation Theorem, Journal of Optimization Theory and Applications, Vol. 36, pp. 451-455, 1982. · Zbl 0452.90072 · doi:10.1007/BF00934357
[11]Arrow, K. J., Barankin, E. W., andBlackwell, D.,Admissible Points of Convex Sets, Contribution to the Theory of Games, Edited by H. W. Kulan and A. W. Tucker, Princeton University Press, Princeton, New Jersey, 1953.
[12]Hartley, R.,On Cone-Efficiency, Cone-Convexity, and Cone-Compactness, SIAM Journal of Applied Mathematics, Vol. 34, pp. 211-222, 1978. · Zbl 0379.90005 · doi:10.1137/0134018
[13]Stoer, J., andWitzgall, L.,Convexity and Optimization in Finite Dimensions, Vol. 1, Springer-Verlag, Berlin, Germany, 1970.