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Compromise solutions, domination structures, and Salukvadze’s solution.(English)Zbl 0362.90111


MSC:

90C30 Nonlinear programming
91A99 Game theory

Cite

References:

[1]Von Neumann, J., andMorgenstern, O.,Theory of Games and Economic Behavior, Princeton University Press, Princeton, New Jersey, 1947. ·Zbl 1241.91002
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[4]Blaquiere, A., Gerard, F., andLeitmann, G.,Quantitative and Qualitative Games, Academic Press, New York, New York, 1969.
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[16]Freimer, M., andYu, P. L.,An Approach Toward Decision Problems with Multiobjectives, University of Rochester, Center for System Science, Report No. 72-03, 1972.
[17]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
[18]MacGrimmon, K. R.,Decision Making Among Multiple-Attribute Alternatives: A Survey and Consolidated Approach, The Rand Corporation, Memorandum No. RM-4823-ARPA, 1963.
[19]Raiffa, H.,Decision Analysis, Addison-Wesley Publishing Company, Reading, Massachusetts, 1968. ·Zbl 0181.21802
[20]Raiffa, H.,Preferences for Multi-Attributed Alternatives, The Rand Corporation, Memorandum No. RM-5868-POT/RC, 1969.
[21]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
[22]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
[23]Stalford, H. L.,Criteria for Pareto-Optimality in Cooperative Differential Games, Journal of Optimization Theory and Applications, Vol. 9, pp. 391-398, 1972. ·Zbl 0225.90059 ·doi:10.1007/BF00934739
[24]Yu, P. L.,A Class of Solutions for Group Decision Problems, Management Science, Vol. 19, pp. 936-946, 1973. ·Zbl 0264.90008 ·doi:10.1287/mnsc.19.8.936
[25]Yu, P. L.,Cone Convexity, Cone Extreme Points and Nondominated Solutions in Decision Problems with Multiobjectives, University of Rochester, Center for System Science, Report No. 72-02, 1972.
[26]Zeleny, M.,Linear Multiobjective Programming, The University of Rochester, Graduate School of Management, Ph.D. Thesis, 1972.
[27]Yu, P. L.,Introduction to Domination Structures in Multicriteria Decision Problems, University of Rochester, Graduate School of Management, System Analysis Program, Series No. F7219, 1972.
[28]Freimer, M., andYu, P. L.,The Application of Compromise Solutions to Reporting Games, University of Rochester, Graduate School of Management, System Analysis Program, Series No. F7220, 1972.
[29]Yu, P. L., andZeleny, M.,The Set of All Nondominated Solutions in the Linear Case and A Multicriteria Simplex Method, University of Rochester, Center for System Sciences, Report No. 73-03, 1973.
[30]Zadeh, L. A.,Optimality and Non-Scalar-Valued Performance Criteria, IEEE Transactions on Automatic Control, Vol. AC-8, pp. 59-60, 1963. ·doi:10.1109/TAC.1963.1105511
[31]DaCuncha, 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
[32]Salukvadze, M. E.,Optimization of Vector Functionals, I, Programming of Optimal Trajectories (in Russian), Avtomatika i Telemekhanika, No. 8, pp. 5-15, 1971. ·Zbl 0236.49019
[33]Salukvadze, M. E.,Optimization of Vector Functionals, II, The Analytic Construction of Optimal Controls (in Russian), Avtomatika i Telemekhanika, No. 9, pp. 5-15, 1971.
[34]Huang, S. C.,Note on the Mean-Square Strategy for Vector-Valued Objective Functions, Journal of Optimization Theory and Applications, Vol. 9, No. 5, pp. 364-366, 1972. ·Zbl 0222.49004 ·doi:10.1007/BF00932935
[35]Leitmann, G.,An Introduction to Optimal Control, McGraw-Hill Book Company, New York, New York, 1966. ·Zbl 0196.46302
[36]Freimer, M., andYu, P. L.,Some New Results on Compromise Solutions, University of Rochester, Graduate School of Management, Series No. F7221, 1972.
[37]Yu, P. L.,Nondominated Investment Policies in Stock Markets (Including an Empirical Study), Unversity of Rochester, Graduate School of Management, Systems Analysis Program, Series No. F7222, 1973.
[38]Shubik, M.,Readings in Game Theory and Political Behavior, Doubleday and Company, New York, New York, 1954.
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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