| Summary: | For optimal control problems of Bolza with variable and free end-points, nonlinear dynamics, nonlinear isoperimetric inequality and equality restrictions, and nonlinear pointwise mixed time-state-control inequality and equality constraints, sufficient conditions for strong minima are derived. The algorithm used to prove the main theorem of the paper includes a crucial symmetric inequality, making this technique an independent self-contained method of classical concepts such as embedding theorems from ordinary differential equations, Mayer fields, Riccati equations, or Hamilton−Jacobi theory. Moreover, the sufficiency theory given in this article is able to detect <i>discontinuous</i> solutions, that is, solutions which need to be neither continuous nor piecewise continuous but only essentially bounded.
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