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Effective content of the calculus of variations I: Semi-continuity and the chattering lemma
Annals of Pure and Applied Logic 78 (1-3):127-146 (1996)
Abstract
The content of existence theorems in the calculus of variations has been explored and an effective treatment of semi-continuity has been achieved. An algorithm has been developed which captures the natural algorithmic content of the notion of a semi-continuous function and this is used to obtain an effective version of the “chattering lemma” of control theory and ordinary differential equations. This lemma reveals the main computational content of the theory of relaxed optimal controlOther Versions
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Citations of this work
Approaches to Effective Semi‐Continuity of Real Functions.Xizhong Zheng, Vasco Brattka & Klaus Weihrauch - 1999 - Mathematical Logic Quarterly 45 (4):481-496.
References found in this work
Nicht konstruktiv beweisbare sätze der analysis.Ernst Specker - 1949 - Journal of Symbolic Logic 14 (3):145-158.
Mazur S.. Computable analysis, edited by Grzegorczyk A. and Rasiowa H., Rozprawy matematyczne no. 33, Państwowe Wydawnictwo Naukowe, Warsaw 1963, 111 pp. [REVIEW]R. L. Goodstein - 1971 - Journal of Symbolic Logic 36 (1):148-150.
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