Abstract
We review approaches to the calculus of variations and optimal control by methods of nonstandard analysis. We present Young’s generalized curves, relaxed controls, versions of Ekeland’s variational principle and of the maximum principle, and nonstandard discretizations of the Euler–Lagrange equations within the Robinson model-theoretic framework (RA) and the Nelson internal set theory (IST). The reader can find a nonstandard treatment of the so-called stochastic calculus of variations in [10].
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