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Necessary and sufficient conditions for local and global nondominated solutions in decision problems with multi-objectives. (English) Zbl 0387.90095

MSC:
90C31 Sensitivity, stability, parametric optimization
90C25 Convex programming
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[1] Zadeh, L. A.,Optimality and Non-Scalar-Valued Performance Criteria, IEEE Transactions on Automatic Control, Vol. AC-8, pp. 59-61, 1963. · doi:10.1109/TAC.1963.1105511
[2] Kuhn, H. W., andTucker, A. W.,Nonlinear Programming, Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, University of California Press, Berkeley, California, 1951.
[3] Tamura, K.,A Method for Constructing the Polar Cone of a Polyhedral Cone, with Application to Linear Multicriteria Decision Problems, Journal of Optimization Theory and Applications, Vol. 19, pp. 547-564, 1976. · Zbl 0309.90029 · doi:10.1007/BF00934654
[4] Vincent, T. L., andLeitmann, G.,Control-Space Properties of Cooperative Games, Journal of Optimization Theory and Applications, Vol. 6, pp. 91-113, 1970. · Zbl 0185.24002 · doi:10.1007/BF00927045
[5] Leitmann, G., Rocklin, S., and Vincent, T. L.,A Note on Control Space Properties of Cooperative Games, Journal of Optimization Theory and Applications, Vol. 9, pp. 379-390, 1972. · Zbl 0235.90059 · doi:10.1007/BF00934738
[6] Reis, R. W., andCitron, S. J.,On Noninferior Performance Index Vectors, Journal of Optimization Theory and Applications, Vol. 7, pp. 11-28, 1971. · Zbl 0204.46803 · doi:10.1007/BF00933589
[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] Mangasarian, O.,Nonlinear Programming, McGraw-Hill Book Company, New York, New York, 1969. · Zbl 0194.20201
[10] Stoer, J., andWitzgall, C.,Convexity and Optimization in Finite Dimensions, I, Springer-Verlag, Berlin, Germany, 1970. · Zbl 0203.52203
[11] Canon, M. D., Cullum, C. D., andPolak, E.,Theory of Optimal Control and Mathematical Programming, McGraw-Hill Book Company, New York, New York, 1970. · Zbl 0264.49001
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