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Local Minimality of a Lipschitz Extremal

Published online by Cambridge University Press:  20 November 2018

Vera Zeidan
Vera Zeidan*
Affiliation:
Department of Mathematics Michigan State University East Lansing, MI USA 48824
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Abstract

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In this paper the question of weak and strong local optimality of a Lipschitz (as opposed to C1 ) extremal is addressed. We show that the classical Jacobi sufficient conditions can be extended to the case of Lipschitz candidates. The key idea for this achievement lies in proving that the “generalized” strengthened Weierstrass condition is equivalent to the existence of a “feedback control” function at which the maximum in the “true” Hamiltonian is attained. Then the Hamilton-Jacobi approach is pursued in order to conclude the result.

Keywords

Primary:49B10
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 44 , Issue 2 , 01 April 1992 , pp. 436 - 448
Copyright
Copyright © Canadian Mathematical Society 1992

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