Abstract
We shall consider situations in which some “decision maker” has to choose, in a set of feasible decisions, a decision which may be considered as the “ best” according to some finite set of criteria.
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Bibliography
J.P. Aubin: “A Pareto Minimum Principle”, in Kuhn, Szego (eds.): “ Differential Games and Related Topics”, North-Holland, 1971.
E. Berge, A. Gouila-Houri: “Programming, Games and Transportation Networks”, Wiley, 1965.
A. Blaquière: “ Vector Valued Optimization in Multiplayer Quantitative Games”, this volume, pp. 33–54, 1976.
A. Blaquière, L. Juricek, K. Wiese: “Geometry of Pareto Equilibria and Maximum Principle in N-Person Differential Games” J. of Lath. An. and Appl. vol. 38, 1972.
G. Birkhoff: “Lattice Theory” American Mathematical Society Colloquium Pubbl.ications vol. X XV, 1948.
S.S.L. Chang: “General Theory of Optimal Processes” J. SIAJ. on Control vol. 4, pp. 46–55, 1966.
K.O. Chu: “On the Noninferior Set for the Systems with Vector-Valued Objective Function” IEEE Tr. on Aut. Contr. AC-15, pp. 103124, 1970.
L.O.Da Cunha, E. Polak: “Constrained Minimization Under Vector-Valued Criteria in Finite Dimensional Spaces” J. of Math. An. and Appl. vol. 19, pp. 103–124, 1967.
G. Debreu: “Theory of Value” Wiley, 1959.
D. Gale: “The Theory of Linear Economic Models”, McGraw-Hill, 1960.
A.H. Geoffrion: “Strictly Concave Parametric Programming, Part I: Basic Theory”, Management Science, vol. 13, pp. 244–253, 1966.
A.H. GeofIrion: “Strictly Concave Parametric Programming, Part II: Additional Theory and Computational. Considerations”, Management Science, vol. 13, pp. 359–370, 1967a.
A.H. Geoffrion: “Solving Bicriterion Mathematical Programs” Op.Res., vol. 15, pp. 39–54, 1967b.
A. Haurie: “On Pareto Optimal Decisions for a Coalition of a Subset of Players” IEEE Tr. on Aut. Contr. AC-18, pp. 144–149, 1973.
A. Haurie, M. C. Delfour: “Individual and Collective Rationality in a Dynamic Pareto Equilibrium”, J.O.T.A. vol. 13, pp. 290–302, 1974.
T. Hoang: “The Farkas-Minkowski Theorem and Extremum Problems”, in J. and M. $os (eds.): “Mathematical Models in Economics”, North-Holland, 1974.
L. Hurwicz: “Programming in Linear Spaces”, in K.J. Arrow, L. Hurwicz, H. Uzawa (eds.): “Studies in Linear and Nonlinear Programming”, Stanford Univ. Press, 1958.
S. Karlin: “Mathematical Methods and Theory in Games, Programming and Economics” vol. 1. Addison-Wesley, 1959.
R.L. Keeney, H. Raiffa: “Decision Analysis with Multiple Conflicting Objectives, Preferences and Value Tradeoffs” II ASA Working Paper WP–75–73, 1975.
A. Klinger: “Vector-Valued Performance Criteria” IEEE Tr. on Aut. Contr. AC-9, pp. 117–118, 1964.
A. Klinger: “Improper Solutions of the Vector Maximum Problem” Op. Res. vol. 15, PP. 570–572, 1967.
T.C. Koopmans (ed.): “Activity Analysis of Production and Allocation”, Cowles Commission Monograph N° 13, Wiley, 1951.
H.W. Kuhn, A.W. Tucker: “Nonlinear Programming” in J. Neyman (ed.): Proc. of the Second Berkeley Symposium on Mathematical Statistics and Probability, Univers. of Calif. Press, pp. 481–491, 1951.
G. Leitmann, S. Rocklin, T.L. Vincent: “A Note on Control-Space Properties of Cooperative Games”, J.O.T.A. vol. 9, 1972.
G. Leitmann, W. Sohmitendorf: “Some Sufficienoy Conditions for Pareto-Optimal Control” J. of Dynamic Systems, Measurement and Control, vol. 95, pp. 356–361, 1973.
G. Leitmann: “Cooperative and Non-Cooperative Many Player Differential Games”, Springer Verlag, 1974.
G. Leitmann: “Cooperative and Non-Cooperative Differential Games’, this volume, pp. 7–32, 1976.
R.D. Luce, H. Raiffa: “Games and Decisions” Wiley, 1957.
K.R. Mao Grimmon: “An Overview of Multiple Objective Decision Making” in J.L. Cochrane, M. Zeleny (eds.): “Multiple Criteria Decision Making”, Univers. of Southern Calif. Press, pp. 18–44, 1973.
O. Mangasarian: “Nonlinear Programming” McGraw-Hill, 1969.
A. Marzollo, W. Ukovich: “A Support Function Approach to the Characterization of the Optimal Gain Vectors in Cooperative Games” Proc. of the 1974 IEEE Conference on Decision and Control, pp. 362–367, 1974.
A. Marzollo, W. Ukovich: “Nondominated Solutions in Cooperative Gamest A Dual Space Approach”, Proc. of the VI IFAC Congress, Boston, 1975.
A. Marzollo, P. Serafini, W. Ukovich: “Decisioni Paretiane e loro determinazione”, in “Teoria dei Sistemi ed Economia” GES -I1 Mulino, 1976.
W. Pareto: “Cours d’Economie Politique” Ronge, 1896.
E. Polak, A.N. Payne: “On Multicriteria Optimization” ERL - M 566 Univ. of Californ., Berkeley, May 1975.
J. Ponstein: “Seven Kinds of Convexity”, SIAM Review, vol. 9, N° 1, 1967.
Z.V. Rekasius, W.E. Schmitendorf: “On the Noninferiority of Nash Equilibrium Solutions” IEEE Tr. on Aut. Contr. AC–16, pp. 170–173, 1971.
R.T. Rockafellar: “Convex Analysis”, Princeton Press, 1970.
B. Roy: “Problems and Methods with Multiple Objective Functions”, Math. Progr.,vol. 1, pp. 239–266, 1971.
W.E. Schmitendorf: “ Cooperative Games and Vector-Valued Criteria Problems” IEEE Tr. on Aut. Contr. AC–18, pp. 139–144, 1973.
A.K. Sen: “Collective Choice And Social Welfare” Oliver and Boyd, 1970.
S. Smale: “Global Analysis and Economics I: Pareto Optimum and a Generalization of Morse Theory”, in M. Peixoto (ed.): Dynamical Systems, pp. 531–544, Academic Press, 1973.
S. Smale: “Global Analysis and Economics V: Pareto Theory with Constraints” J. of Math. Economics, vol. 1, pp. 213–221, 1974.
W. Stadler: “Preference Optimality and Applications of Pareto Optimality”, this volume.
A.W. Starr, Y.C. Ho: “Nonzero-Sum Differential Games” J.O.T.A., vol. 3, pp. 184–206, 1969a.
A.W. Starr, Y.C. Ho: “Further Properties of Nonzero-Sum Differential Games” J.O.T.A., vol. 3, pp. 207–219, 1969b.
T.L. Vincent, G. Leitmann: “Control-Space Properties of Cooperative Games” J.O.T.A., vol. 6, pp. 91–104, 1970.
Y.H. Wan: “On Local Pareto Optimum” J. of Math. Economics, vol. 2, 1975.
P.L. Yu: “Cone Convexity, Cone Extreme Points and Nondominated Solutions in Decision Problems with Multiobjectives”, University of Rochester, Center for System Science, Report 72–02, 1972, reprinted in J.O.T.A., 1974.
P.L. Yu: “Domination Structures and Nondominated Solutions”, this volume.
L.A. Zadeh: “Optimality and Non-Scalar-Valued Performance Criteria” IEEE Tr. on Aut. Contr. AC–8, pp. 59–60, 1963.
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Marzollo, A., Ukovich, W. (1975). On Some Broad Classes of Vector Optimal Decisions and Their Characterization. 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_6
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DOI: https://doi.org/10.1007/978-3-7091-2438-3_6
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