Abstract
It is shown that standard algebraic and analytic methods lead to the correct solution of the constrained optimization problem. The extra term in the second variation, discussed in a recent paper by Hull (Ref. 1), arises naturally from elementary calculus. It is present if, and only if, the variables of the objective function are dependent, but this is always the case for constrained optimization. Second and higher variations in the performance index, rather than in the augmented performance index, are considered.
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References
Hull, D. G.,On the Variational Process in Parameter Optimization, Journal of Optimization Theory and Applications, Vol. 56, pp. 31–38, 1988.
Walsh, G. R.,Methods of Optimization, John Wiley and Sons, Chichester, Sussex, England, 1979.
Phillips, E. G.,A Course of Analysis, 2nd Edition, Cambridge University Press, Cambridge, England, 1948.
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Communicated by L. C. W. Dixon
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Anderson, N., Arthurs, A.M. & Walsh, G.R. On the variational process in parameter optimization. J Optim Theory Appl 61, 311–314 (1989). https://doi.org/10.1007/BF00962803
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DOI: https://doi.org/10.1007/BF00962803