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


MSC:

90C25 Convex programming
93B05 Controllability
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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.
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[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
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[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.
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[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
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