First- and second-order necessary conditions with respect to components for discrete optimal control problems

This paper is devoted to the study of discrete optimal control problems. We aim to obtain more constructive optimality conditions under weakened convexity assumptions. Based on a new approach introduced in this work, an optimality condition with respect to every component is obtained in the form of...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2020-01, Vol.364, p.112342, Article 112342
Main Authors: Mardanov, Misir J., Melikov, Telman K., Malik, Samin T., Malikov, Kamran
Format: Article
Language:English
Subjects:
Discrete maximum principle with respect to components
Necessary conditions
Optimal control
Second-order optimality conditions
Singular and quasi-singular controls with respect to components
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Summary:This paper is devoted to the study of discrete optimal control problems. We aim to obtain more constructive optimality conditions under weakened convexity assumptions. Based on a new approach introduced in this work, an optimality condition with respect to every component is obtained in the form of a global maximum principle. In addition, an optimality condition with respect to one of the components of a control in the form of the global maximum principle and with respect to another component of a control in the form of the linearized maximum principle are obtained. Furthermore, various second-order optimality conditions in terms of singular and quasi-singular controls with respect to the components are obtained on the fly.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2019.112342