Abstract
Typical problems in system design, decision making, decentralized control, etc., and most multi-person games bear the following general formulation of multiple-objective (MO) optimization problems:
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References
L. A. Zadeh, “Optimality and Non-Scalar-Valued Performance Criteria,” IEEE Trans, Automat. Contr., vol. AC-8, pp. 59–60, Jan. 1963.
J. Von Neumann and O. Morgenstern, Theory of Games and Economic Behavior, 3rd ed. Princeton: Princeton Univ. Press, 1953.
Y.C. Ho, “Differential Games, Dynamic Optimization, and Generalized Control Theory,” J. Optimiz. Theory Appl. vol. 6, no. 3, pp. 179–209, 1970.
J. G. Lin, “On N-Person Cooperative Differential Games,” Proc. 6th Princeton Conf. Inform. Sci. Amp; Syst., Princeton, N.J., pp. 502–507, Mar. 1972.
T. C. Koopmans, “Analysis of Production as an Efficient Combination of Activities,” Activity Analysis of Production and Allocation, T. C. Koopmans, Ed. New York: Wiley, pp. 33–97, 1951.
K.J. Arrow, E. W. Barankin, and D. Blackwell, “Admissible Points of Convex Sets,” Contributions to the Theory of Games, vol.II, H. W. Kuhn and A. W. Tucker, Eds. Princeton: Princeton Univ. Press, pp. 87–91, 1953.
N.O. Da Cuncha and E. Polak, “Constrained Minimization under Vector-Valued Criteria in Finite Dimensional Spaces,” J. Math. Anal. and Appl. vol.19, no.1, pp.103–124, July 1967.
J. G. Lin, “Multiple-Objective Optimization,” Columbia Univ., Dept. of Elect. Eng. & Comp. Sci., Syst. Res. Gr. Tech. Rept, Dec. 1972.
G. A. Katopis and J. G. Lin, “Non-Inferiority of Controls under Double Performance Objectives: Minimal Time and Minimal Energy,” Proc. 7th Hawaii Int. Conf. Syst. Sci., Honolulu, Hawaii, pp. 129–131, Jan. 1974.
J. G. Lin, “Circuit Design under Multiple Performance Objectives,” Proc. 1974 IEEE Int. Symp. Circuits & Systems, San Francisco, Calif., pp. 549–552, Apr. 1974.
J.G. Lin, “Maximal Vectors and Multi-Objective Optimization,” J. Optimiz. Theory Appl., vol.18, no.1, pp.41–64, Jan. 1976.
J.G. Lin, “Proper Equality Constraints (PEC) and Maximization of Index Vectors,” J. Optimiz. Theory Appl. vol.20, no.4, Dec.1976.
J.G. Lin, “Proper Inequality Constraints (PIC) and Maximization of Index Vectors” to appear in J. Optimiz. Theory Appl..
J.G. Lin, “Multiple-Objective Problems: Pareto-Optimal Solutions by Method of Proper Equality Constraints (PEC),” to appear in IEEE Trans. Automatic Control.
J. G. Lin, “Multiple-Objective Programming: Lagrange Multipliers and Method of Proper Equality Constraints,” to be presented in 1976 Joint Automatic Control Conf., July 1976.
P.L. Yu, “Cone Convexity, Cone Extreme Points, and Nondominated Solutions in Decision Problems with Multi-objectives,” J. Optimiz. Theory Appl. vol.14, no.3, pp.319–377, Sept. 1974.
H. Payne, E. Polak, D. C. Collins, and W.S. Meisel, “An Algorithm for Bicriteria Optimization Based on the Sensitivity Function.” IEEE Trans. Automat. Contr. vol. AC-20, no. 4, pp. 546–548, Aug. 1975.
J. M. Holtzman and H. Halkin, “Directional Convexity and the Maximum Principle for Discrete Systems,” J. SIAM Contr., vol.4, no. Z, pp. Z63–Z75, 1966.
D. M. Himmelblau, Applied Nonlinear Programming, New York: McGraw-Hill, 1972.
A. E. Bryson and Y. C. Ho, Applied Optimal Control, Waltham, Mass.: Blaisdell, 1969.
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Lin, J.G. (1976). Three Methods for Determining Pareto-Optimal Solutions of Multiple-Objective Problems. In: Ho, Y.C., Mitter, S.K. (eds) Directions in Large-Scale Systems. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-2259-7_9
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DOI: https://doi.org/10.1007/978-1-4684-2259-7_9
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