Abstract
To a layman one might explain the meaning of “optimization” as follows: Consider any process whatever which may be described mathematically, and whose outcome may be influenced by a set of possible decisions. Associate with the process a numerical criterion whose value depends on the decision and corresponding outcome of the process. “Optimization” then means that the decision is to be made so as to yield a maximum or a minimum numerical value of the criterion; that is, the criterion serves as a means of comparing different decisions and their outcomes.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Yu, P.L. and Leitmann, G., Compromise solutions, domination structures and Salukvadze’s solution, J. of Optimization Theory and Applications, 13, 362, 1973.
Stadler, W., Preference optimality, to be published.
Stadler, W., Sufficient conditions for preference optimality, to appear in J. of Optimization Theory and Applications, 1975.
Lee, E.B. and Markus, L., Foundations of Optimal Control Theory, John Wiley and Sons, New York, 1967.
Debreu, G., Theory of Value, John Wiley and Sons, New York, 1959.
Samuelson, P.A., Economics, ninth ed., McGraw-Hill, New York, 1969.
Mangasarian, O. I., Nonlinear Programming, McGraw-Hill, New York, 1969.
Fishburn, P.C., Utility Theory for Decision Making, John Wiley and Sons, 1970.
Debreu, G., Smooth preferences, Econometrica, 40, 603, 1972.
Matsushima, Y., Differential Manifolds, translated from the Japanese by Kobayashi, E.T., Marcel Dekker, Inc., New York, 1972.
Spivak, M., Differential Geometry, I and II, Publish or Perish, Inc., 6 Beacon St., Boston, Mass. 02108 (USA), 1970.
Debreu, G., Representation of a preference ordering by a numerical function, in Decision Processes, Thrall, R.M., Coombs, C.H. and Davis, R.L., Eds., John Wiley and Sons, New York, 1954.
Fishburn, P.C., Lexicographic orders, utilities and decision rules: a survey, Management Science, 20, 1442, 1974.
Eilenberg, S., Ordered topological spaces, Amer. J. of Math., 63, 39, 1941.
Rader, J.T., The existence of a utility function to represent preferences, The Review of Economic Studies, 30, 229, 1963.
Debreu, G., Continuity properties of Paretian utility, Int’l Economic Review, 5, 285, 1964.
de Finetti, B., Sulle stratifiazioni convesse, Annali di Matematica Pura ed Applicata, 4, 173, 1949.
Fenchel, W., Convex Cones, Sets and Functions, mimeographed notes, Department of Mathematics, Princeton University, 1953.
Fenchel, W., Uber konvexe Funktionen mit vorgeschriebenen Niveau mannigfaltigkeiten, Mathematische Zeitschrift, 63, 496, 1956.
Long, R.S., Newton-Raphson operator; problems with undetermined end points, J. of the Amer. Inst. of Aeronautics and Astronautics, 3, 1351, 1965.
Leitmann, G., Einführung in die Theorie optimaler Steuerung and der Differentialspiele, translated from the English by Stadler, W., R. Oldenbourg Verlag, Munich, 1974.
Willard, S., General Topology, Addison-Wesley, Reading, Mass., 1970.
Yu, P.L., Cone convexity, cone extreme points, and nondominated solutions in decision problems with multiobjectives, J. of Optimization Theory and Applications, 14, 319, 1974.
Yu, P.L. and Leitmann, G., Nondominated decisions and cone convexity in dynamic multicriteria decision problems, J. of Optimization Theory and Applications, 14, 573, 1974.
Aumann, R.J., Values of markets with a continuum of traders, Technical Report no. 121, The Economics Series, Institute for Mathematical Studies in the Social Sciences, Stanford University, Stanford, 1974.
Salama, A.I.A. and Gourishankar, V., Optimal control of systems with a single control and several cost functionals, Int’l J. of Control, 14, 705, 1971.
Leitmann, G. and Stadler, W., Cooperative games for the experimentalist, Nonlinear Vibration Problems (Zagadnienia Organ Nieliniowych), Polish Academy of Sciences, 15, 273, 1974.
Stadler, W., Natural structures, in preparation.
Fox, E.A., Mechanics, Harper and Row, New York, 1967.
Athans, M. and Falb, P.L., Optimal Control, McGraw-Hill, New York, 1966.
Da Cunha, N.O. and Polak, E., Constrained minimization under vector-valued criteria in finite dimensional spaces, J. of Mathematical Analysis and Applications, 19, 103, 1967.
Truesdell, C. and Noll, W., The Nonlinear Field Theories of Mechanics, Handbuch der Physik, III/3, Springer Verlag, 1965.
Antmann, S.S., The Theory of Rods, Handbuch der Physik, VIa/2, Springer Verlag, 1972.
Sokolnikoff, I.S., Mathematical Theory of Elasticity, McGraw-Hill, New York, 1956.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1975 Springer-Verlag Wien
About this chapter
Cite this chapter
Stadler, W. (1975). Preference Optimality and Applications of Pareto-Optimality. In: Leitmann, G., Marzollo, A. (eds) Multicriteria Decision Making. International Centre for Mechanical Sciences, vol 211. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2438-3_4
Download citation
DOI: https://doi.org/10.1007/978-3-7091-2438-3_4
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-81340-9
Online ISBN: 978-3-7091-2438-3
eBook Packages: Springer Book Archive