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