×

zbMATH — the first resource for mathematics

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

MSC:
90C31 Sensitivity, stability, parametric optimization
PDF BibTeX XML Cite
Full Text: DOI
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. · Zbl 0193.18401
[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. · Zbl 0050.14203
[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. · Zbl 0203.52203
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.