Strong Minimizers of the Calculus of Variations on Time Scales and the Weierstrass Condition

Details Strong Minimizers of the Calculus of Variations on Time Scales and the Weierstrass Condition Strong Minimizers of the Calculus of Variations on Time Scales and the Weierstrass Condition

2009-05-12

arxiv.org/abs/0905.1870v1

Proceedings of the Estonian Academy of Sciences, Vol. 58, no. 4, 2009, 205--212

Mathematics

Optimization and Control

Paper accepted 12/May/2009 for publication in the Proceedings of the Estonian Academy of Sciences

Scientific paper

10.3176/proc.2009.4.02

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.

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