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


Mardanov M. J., Melikov T. K., Malik S. T., Məlikov K.

Journal of Computational and Applied Mathematics, vol.364, 2020 (SCI-Expanded, Scopus)

  • Publication Type: Article / Article
  • Volume: 364
  • Publication Date: 2020
  • Doi Number: 10.1016/j.cam.2019.112342
  • Journal Name: Journal of Computational and Applied Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, Computer & Applied Sciences, INSPEC, MathSciNet, Metadex, zbMATH, DIALNET, Civil Engineering Abstracts
  • Keywords: Discrete maximum principle with respect to components, Necessary conditions, Optimal control, Second-order optimality conditions, Singular and quasi-singular controls with respect to components
  • Open Archive Collection: Article
  • Azerbaijan State University of Economics (UNEC) Affiliated: Yes

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.