Abstract
A dual extremum principle for the Verhulst-Pearl population equation is constructed using a complementary variational technique. The dual formulation utilizes a minimum principle recently developed by Leitmann to convert the functional optimization problem into a parameter optimization problem.
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Leitmann, G.,A Minimum Principle for a Population Equation, Journal of Optimization Theory and Applications, Vol. 9, No. 2, 1972.
Chan, W. L., Leininger, G. G., andFarison, J. B.,Complementary Variational Principle and Duality in Mathematical Programming, Journal of Mathematical Analysis and Applications, Vol. 43, No. 2, 1973.
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Communicated by G. Leitmann
This research was supported in part by NASA Grant No. NGR-36-010-024. The first author would like to thank Dr. W. Stadler, Department of Mechanical Engineering, University of California, Berkeley, for his valuable suggestions.
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Chan, W.L., Leininger, G.G. A dual extremum principle for a population equation. J Optim Theory Appl 13, 490–492 (1974). https://doi.org/10.1007/BF00934943
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DOI: https://doi.org/10.1007/BF00934943