Abstract
The exact penalty method is applied to the problem of optimal control of a system described by ordinary differential equations. Though the functional thus obtained is essentially nonsmooth, it is direction differentiable (and even subdifferentiable). Differential equations are regarded as constraints and “eliminated” by introducing a penalty function. The aim of this paper is to show the well-known conditions of optimality can be derived via penalty functions.
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REFERENCES
Demyanov, V.F., Giannessi, F., and Karelin, V.V., Optimal Control Problems via Exact Penalty Functions, J. Global Optimiz., 1998, vol. 12, no 3, pp. 215–223.
Eremin, I.I., The Penalty Method in Convex Programming, Dokl. Akad. Nauk SSSR, 1967, vol. 173, pp. 748–751.
Zangwill, W.L., Nonlinear Programming via Penalty Functions, Manag. Sci., 1967, vol. 13, pp. 344–358.
Fletcher, R., Penalty Functions, in Mathematical Programming: The-State-of-the-Art, Bachen, A., Grötschel, M., and Korte, B., Eds., Berlin: Springer-Verlag, 1983, pp. 87–11.
Di Pillo, G. and Grippo, L., On the Exactness of a Class of Nondifferentiable Penalty Functions, J. Optimiz. Theory Appl., 1988, vol. 57, pp. 397–408.
Demyanov, V.F., Di Pillo, G., and Facchinei F., Exact Penalization via Dini and Hadamard Constraint Derivatives, Optimiz. Meth. Software, 1998, vol. 9, pp. 19–36.
Demyanov, V.F. and Rubinov, A.M., Osnovy negladkogo analiza i kvazidifferentsial'noe ischislenie (Elements of Nonsmooth Analysis and Quasidifferential Calculus), Moscow: Nauka, 1990.
Hartman, P., Ordinary Differential Equations, New York: Wiley, 1964. Translated under the title Obyknovennye differentsial'nye uravneniya, Moscow: Mir, 1979.
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Karelin, V.V. Penalty Functions in a Control Problem. Automation and Remote Control 65, 483–492 (2004). https://doi.org/10.1023/B:AURC.0000019381.32610.e9
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DOI: https://doi.org/10.1023/B:AURC.0000019381.32610.e9