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

Mardanov, Misir J., Melikov, Telman K., Malik, Samin T. and Malikov, Kamran (2019) First- and second-order necessary conditions with respect to components for discrete optimal control problems. Journal of Computational and Applied Mathematics, 364, [112342]. (doi:10.1016/j.cam.2019.112342).

Record type: Article

Abstract

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.

Text

JCAM2020 - Accepted Manuscript

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