Abstract
In this paper some simple ideas about ordered sets and inverse functions are developed into a theory of inverse pairs of optimization problems. This relationship is shown to permit the use of root-finding methods to find a solution for one problem through a sequence of solutions to the other. A variety of problems showing this relationship are presented as examples.
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References
R.A. Blau, “On some optimization problems under uncertainty”, Doctoral Thesis, Technical Report 49, Department of Statistics, Carnegie-Mellon, Pittsburgh (1971).
R.G. Cassidy, C.A. Field and M.J.L. Kirby, “Solution of a satisficing model for random payoff games”,Management Science 19 (1972) 266–271.
D. Gale,Theory of linear economic models (McGraw-Hill, New York, 1960).
A. Geoffrion, “Stochastic programming with aspiration or fractile criteria”,Management Science 13 (1967) 672–679.
J. Philip, “Algorithms for the vector maximization problem”,Mathematical Programming 2 (1972) 207–229.
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This research was partially supported by the National Research Council of Canada under grants A7675 and A7751.
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Cassidy, R.G., Field, C.A. & Sutherland, W.R.S. Inverse programming: Theory and examples. Mathematical Programming 4, 297–308 (1973). https://doi.org/10.1007/BF01584672
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DOI: https://doi.org/10.1007/BF01584672