Abstract
A general multiplier rule which is an extension of the multiplier rule given by Hestenes is proved. This multiplier rule is applied to obtain the necessary conditions given by Neustadt for a solution to a canonical optimization problem which includes many optimal control problems as special cases.
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References
Hestenes, M. R.,Calculus of Variations and Optimal Control Theory, John Wiley and Sons, New York, 1966.
Hestenes, M. R.,On Variational Theory and Optimal Control Theory, SIAM Journal on Control, Vol. 3, No. 1, 1965.
Neustadt, L. W.,An Abstract Variational Theory with Applications to a Broad Class of Optimization Problems, I, General Theory, SIAM Journal on Control, Vol. 4, No. 3, 1966.
Gamkrelidze, R. V.,On Some Extremal Problems in the Theory of Differential Equations with Applications to the Theory of Optimal Control, SIAM Journal on Control, Vol. 3, No. 1, 1965.
Neustadt, L. W.,An Abstract Variational Theory with Applications to a Broad Class of Optimization Problems, II, Applications, SIAM Journal on Control, Vol. 5, No. 1, 1967.
Gittleman, A.,Dual Formulations of Variational and Optimal Control Problems, University of California at Los Angeles, Ph.D. Thesis, 1969.
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Communicated by M. R. Hestenes
This research is part of a dissertation submitted in partial satisfaction of the requirements for the Ph.D. degree in mathematics at the University of California, Los Angeles. The author would like to express his appreciation to Dr. M. R. Hestenes for his guidance.
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Gittleman, A. A general multiplier rule. J Optim Theory Appl 7, 29–38 (1971). https://doi.org/10.1007/BF00933590
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DOI: https://doi.org/10.1007/BF00933590