J Austral Math Soc Ser B 37 pp354--391, 1996.

On solution sets of nonconvex Darboux problems and applications to optimal control with endpoint constraints

H. D. Tuan

Abstract

We prove a continuous version of a relaxation theorem for the nonconvex Darboux problem x_tt Î F(t, t, x, x_t , xt). This result allows us to use Warga's open mapping theorem for deriving necessary conditions in the form of a maximum principle for optimization problems with endpoint constraints. Neither constraint qualification nor regularity assumption is supposed.

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Author

H. D. Tuan

Institute of Mathematics, P.O. Box 631, Bo Ho, Hanoi, Vietnam.
Present address: Dept. of Electronic-Mechanical Eng., Nagoya University, Nagoya 464-01, Japan.