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On an extremum problem

Published online by Cambridge University Press:  17 February 2009

Joanna Matula
Joanna Matula
Affiliation:
Institute of Mathematics, Lodz University, u1. Stefana Banacha 22, 90–238 Lodz, Poland.
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Abstract

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We consider an optimization problem in which the function being minimized is the sum of the integral functional and the full variation of control. For this problem, we prove the existence theorem, a necessary condition in an integral form and a local necessary condition in the case of monotonic controls.

Type
Research Article
Information
The ANZIAM Journal , Volume 28 , Issue 3 , January 1987 , pp. 376 - 392
Copyright
Copyright © Australian Mathematical Society 1987

References

[1]Cesari, L., Optimization—theory and applications, (Springer-Verlag, New York, 1983).CrossRefGoogle Scholar
[2]Chuprun, B. E., “Zadachi s ogranicheniyem na izmeneniye upravleniya”, Automat i Telemekh. 3 (1975), 24–37.Google Scholar
[3]Golusin, G. M., Geometricheskaja teoriya funktsii kompleksnogo peremennogo (Nauka, Moskva, 1966).Google Scholar
[4]Ioffe, A. D. and Tikhomirov, V. M., Theory of extremal problems, (North-Holland, New York, 1979).Google Scholar
[5]Ioffe, A. D., “On Lower Semicontinuity of Integral Functionals”, SIAM J. Control Optim. 15 (1977).Google Scholar
[6]Krasovskiy, N. N., Teoriya upravleniya dvizheniem, (Nauka, Moskva, 1968).Google Scholar
[7]Mikolajczyk, L. and Walczak, S., “Application of the extremum principle to investigating certain extremal problems”, Trans. Amer. Math. Soc. 259 (1980).CrossRefGoogle Scholar
[8]Noussair, E. S., “On the existence of piecewise continuous optimal controls”, J. Austral. Math. Soc. Ser. B 20 (1977), 31–37.CrossRefGoogle Scholar
[9]Pfaltzgraff, J. and Pinchuk, B., “A Variational Method for Classes of Meromorphic Functions”, J. Analyse Math. (1971), 101–150.CrossRefGoogle Scholar
[10]Sztajnic, J., “Necessary conditions for existence of extremum for controls with bounded variation”, Bull. Soc. Sci. Lett. Lódź, 28, 12 (1978).Google Scholar
[11]Walczak, S., “Euler-Lagrange's conditions for controls with bounded variation”, Control Cybernet. 8 (1979).Google Scholar