Abstract
Two important solution concepts in the theory of multicriteria decision making are Pareto optimum and Lexicographic optimum.
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References
Abrams, R. A., Kerzner, L.: “A simplified test for optimality”, J. of Optimization Theory and Application, 25 (1978) 161–170.
Arrow, K. J.: “An extension of the basic theorems of classical Welfare Economics”, Proceedings of the Second Berkeley Symposium on Mathematical Statistic and Probability (J. Neyman, Editor), University of California Press, Berkeley, CA., 1951.
Ben-Israel, A., Ben-Tal, A., and Charnes, A.: “Necessary and sufficient conditions for a Pareto optimum in convex programming”, Econometrica, 45, (1977), 811–820.
Ben-Israel, A., Ben-Tal, A., and S. Zlobec: “Optimality conditions in convex programming”, in Survey of Mathematical Programming (A. Prekopa, Editor), Hungarian Academy of Science and North-Holland, (1979).
Ben-Tal, A., Ben-Israel, A., and Zlobec, S.: “Characterization of optimality in convex programming without a constraint qualification”, Journal of Optimization Theory and Application, 20, (1976), 417–437.
Ben-Tal, A., and Zlobec, S.: “Convex programming and the lexicographic multicriteria problem”, Mathematische Operationsforschung und Statistik, series Optimization, 8, No. 1 (1977) 61–73.
Charnes, A., and Cooper, W. W.: Management Models and Industrial Application of Linear Programming, Vol. 1, John Wiley & Sons, New York, (1961).
Cenzor, Y.: “Pareto-optimality in multiobjective problems”, Applied Mathematics and Optimization, 4 (1977), 41–59.
Debreu, G.: Theory of Value, An Axiomatic Analysis of Economic Equilibrium, John Wiley 8 Son, New York, 1959.
Dubovitskii, A. Ya. and Milyutin, A. A., “The extremum problem in the presence of constraints”, (Russian), Doklady Akademije Nauk SSSR, 149, (1963), 759–762.
Ferguson, T. S.: Mathematical Statistics: a Decision Theoretic Approach, Academic Press, New York, 1967.
Karlin, S.: Mathematical Methods and Theory in Games, Programming, and Economics, Vol. 1, Addison-Wesley, Reading, Mass. 1959.
Koopmans, T. C.: Activity Analysis of Production and Allocation, T. C. Koopmans (ed.), John Wiley, New York (1951) 33–97.
Penissi, E. J.: “An indirect sufficiency proof for the problem of Lagrange with differential inequalities as added side conditions”, Transactions of American Math. Soc., 14 (1953), 177–198.
Smale, S.: “Sufficient conditions for an optimum”, Warwick Dynamical System 1974 (Lecture Note in Mathematics, Sprmger-Verlag, 1975).
Wan, Y. H.: “On local Pareto optima”, Journal of Mathematical Economics, 2, (1975) 35–42.
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© 1980 Springer-Verlag Berlin Heidelberg
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Ben-Tal, A. (1980). Characterization of Pareto and Lexicographic Optimal Solutions. In: Fandel, G., Gal, T. (eds) Multiple Criteria Decision Making Theory and Application. Lecture Notes in Economics and Mathematical Systems, vol 177. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-48782-8_1
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DOI: https://doi.org/10.1007/978-3-642-48782-8_1
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