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Simple nonlinear dual control problems

Published online by Cambridge University Press:  17 February 2009

J. M. Murray
J. M. Murray
Affiliation:
Department of Applied Mathematics, University of New South Wales, P. O. Box 1, Kensington, N.S.W. 2033.
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Abstract

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In this paper we consider a simple, nonlinear optimal control problem with sufficient convexity to enable us to formulate its dual problem. Both primal and dual problems will include constraints on both the states and controls. The constraints in one problem may cause the “optimal” dual states to be discontinuous. However, we will look at conditions under which the presence of constraints does not force discontinuities and the optimal states and costates are absolutely continuous.

Type
Research Article
Information
The ANZIAM Journal , Volume 27 , Issue 2 , October 1985 , pp. 131 - 144
Copyright
Copyright © Australian Mathematical Society 1985

References

[1]Bodo, E. P. and Hanson, M. A., “A class of continuous nonlinear complementarity problems”, J. Optim. Theory Appl. 24 (1978), 243–262.CrossRefGoogle Scholar
[2]Farr, W. H. and Hanson, M. A., “Continuous time programming with nonlinear constraints”, J. Math. Anal. Appl. 45 (1974), 96–115.CrossRefGoogle Scholar
[3]Grinold, R. C., “Continuous programming, part two: nonlinear objectives”, J. Math. Anal. Appl. 27 (1969), 639–655.CrossRefGoogle Scholar
[4]Hanson, M. A. and Mond, B., “A class of continuous convex programming problems”, J. Math. Anal. Appl. 22 (1968), 427–437.CrossRefGoogle Scholar
[5]Mangasarian, O. L., Nonlinear programming (McGraw-Hill, New York, 1969).Google Scholar
[6]Murray, J. M., “Some existence and regularity results for dual linear control problems”, to appear in J. Math. Anal. Appl.Google Scholar
[7]Rockafellar, R. T., Convex Analysis (Princeton University Press, Princeton, N. J., 1970).CrossRefGoogle Scholar
[8]Rockafellar, R. T., “Conjugate convex functions in optimal control and the calculus of variations”, J. Math. Anal. Appl. 32 (1970), 174–222.CrossRefGoogle Scholar
[9]Rockafellar, R. T., “Existence and duality theorems for convex problems of Bolza”, Trans. Amer. Math. Soc. 159 (1971), 1–40.CrossRefGoogle Scholar
[10]Rockafellar, R. T., “Existence theorems for general control problems of Bolza and Lagrange”, Adv, in Math. 15 (1975), 312–333.CrossRefGoogle Scholar
[11]Rockafellar, R. T., “Integral functionals, normal integrands and measurable selections”, in Nonlinear Operators and the Calculus of Variations (Waelbroeck, L., ed.), (Springer-Verlag, 1976), 157–207.CrossRefGoogle Scholar