Agnieszka B. Malinowska, Delfim F. M. Torres
tlooto Summary
Strong minimizers of the calculus of variations on time scales and the Weierstrass condition are introduced, enabling generalization to both continuous-time and discrete-time conditions.
Abstract
We introduce the notion of strong local minimizer for the problems of the calculus of variations on time scales. Simple examples show that on a time scale a weak minimum is not necessarily a strong minimum. A time scale form of the Weierstrass necessary optimality condition is proved, which enables to include and generalize in the same result both continuous-time and discrete-time conditions.
Citation format
MALINOWSKA, Agnieszka B.; TORRES, Delfim F. M. Strong minimizers of the calculus of variations on time scales and the weierstrass condition [preprint]. arXiv, 2009. arXiv:0905.1870.