Sufficient Optimality Conditions for Optimal Control Problems with State Constraints. (11th June 2019)

• Record Type: Journal Article
• Authors: Antunes de Oliveira, Valeriano; Nunes Silva, Geraldo
• Is Part Of: Numerical functional analysis and optimization. Volume 40:Number 8(2019)
• Page Start: 867
• Page End: 887
• Publication Date: 2019-06-11
• Subjects: Generalized convexity -- optimal control -- state constraints -- sufficient optimality conditions; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2018.1562469
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: It is well-known in optimal control theory that the maximum principle, in general, furnishes only necessary optimality conditions for an admissible process to be an optimal one. It is also well-known that if a process satisfies the maximum principle in a problem with convex data, the maximum principle turns to be likewise a sufficient condition. Here an invexity type condition for state constrained optimal control problems is defined and shown to be a sufficient optimality condition. Further, it is demonstrated that all optimal control problems where all extremal processes are optimal necessarily obey this invexity condition. Thus optimal control problems which satisfy such a condition constitute the most general class of problems where the maximum principle becomes automatically a set of sufficient optimality conditions.