×

zbMATH — the first resource for mathematics

Cone convexity, cone extreme points, and nondominated solutions in decision problems with multiobjectives. (English) Zbl 0268.90057

MSC:
90C25 Convex programming
93B05 Controllability
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Yu, P. L.,The Set of All Nondominated Solutions in Decision Problems with Multiobjectives, University of Rochester, Systems Analysis Program, Working Paper Series, No. F-71-32, 1971.
[2] Luce, R. D., andRaiffa, H.,Games and Decision, John Wiley and Sons, Inc., New York, New York, 1967.
[3] MacGrimmon, K. R.,Decision Making Among Multiple-Attribute Alternatives: A Survey and Consolidated Approach, The RAND Corporation, Memorandum No. RM-4823-ARPA, 1968.
[4] Raiffa, H.,Preferences for Multi-Attributed Alternatives, The RAND Corporation, Memorendum No. RM-5868-DOT/RC, 1969.
[5] DaCunha, N. O., andPolak, E.,Constrained Minimization Under Vector-Valued Criteria in Finite Dimensional Space, Journal of Mathematical Analysis and Applications, Vol. 19, pp. 103-124, 1967. · Zbl 0154.44801 · doi:10.1016/0022-247X(67)90025-X
[6] Ceoffrion, A. M.,Strictly Concave Parametric Programming, Parts I and II, Management Science, Vol. 13, pp. 244-253 and pp. 359-370, 1967. · Zbl 0143.42604 · doi:10.1287/mnsc.13.3.244
[7] Geoffrion, A. M.,Solving Bicriterion Mathematical Programs, Operations Research, Vol. 15, pp. 39-54, 1967. · Zbl 0173.21602 · doi:10.1287/opre.15.1.39
[8] 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
[9] 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
[10] Blackwell, D., andGirshick, M. A.,Theory of Games and Statistical Decisions, John Wiley and Sons, New York, New York, 1954. · Zbl 0056.36303
[11] Ferguson, T. S.,Mathematical Statistics, A Decision Theoretic Approach, Academic Press, New York, New York, 1967. · Zbl 0153.47602
[12] Stoer, J., andWitzgall, C.,Convexity and Optimization in Finite Dimensions I, Springer-Verlag, New York, New York, 1970. · Zbl 0203.52203
[13] Yu, P. L.,A Class of Solutions for Group Decision Problems, Management Science, Vol. 19, pp. 936-946, 1974. · Zbl 0264.90008 · doi:10.1287/mnsc.19.8.936
[14] Mangasarian, O. L.,Nonlinear Programming, McGraw-Hill Book Company, New York, New York, 1969.
[15] Leitmann, G., Rocklin, S., andVincent, 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
[16] Yu, P. L. andZeleny, M.,The Set of All Nondominated Solutions in the Linear Case and a Multicriteria Simplex Method, Journal of Mathematical Analysis and Applications (to appear).
[17] Yu, P. L., andLeitmann, G.,Nondominated Decisions and Cone Convexity in Dynamic Multicriteria Decision Problems, Journal of Optimization Theory and Applications (to appear). · Zbl 0365.90126
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.