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Second-order optimality conditions for the Bolza problem with path constraints

Wood, L. J. (1973) Second-order optimality conditions for the Bolza problem with path constraints. In: 1973 IEEE Conference on Decision and Control including the 12th Symposium on Adaptive Processes. IEEE , Piscataway, NJ, pp. 606-613. https://resolver.caltech.edu/CaltechAUTHORS:20170809-163449641

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Abstract

A set of sufficient conditions for a weak minimum is derived for a form of the nonsingular Bolza problem of variational calculus, with interior point constraints and discontinuities in the system equations. Generalized versions of the conjugate point/focal point, normality, convexity and nontangency conditions associated with the ordinary Bolza problem are obtained. The resulting set of sufficient conditions is minimal, in that only minor modifications are required in order to obtain necessary conditions for normal, nonsingular problems of this form. These conditions are relatively easy to implement. Analogous second-order optimality conditions for problems with natural corners or control constraints are also obtained. Previously stated sufficiency conditions for problems with control constraints are shown to be unnecessarily restrictive, in some cases.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.1109/CDC.1973.269232DOIArticle
http://ieeexplore.ieee.org/document/4045145/PublisherArticle
Additional Information:© 1973 IEEE.
DOI:10.1109/CDC.1973.269232
Record Number:CaltechAUTHORS:20170809-163449641
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170809-163449641
Official Citation:L. J. Wood, "Second-order optimality conditions for the Bolza problem with path constraints," 1973 IEEE Conference on Decision and Control including the 12th Symposium on Adaptive Processes, San Diego, CA, USA, 1973, pp. 606-613. doi: 10.1109/CDC.1973.269232
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:80045
Collection:CaltechAUTHORS
Deposited By: Kristin Buxton
Deposited On:10 Aug 2017 00:02
Last Modified:15 Nov 2021 17:52

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