Analyzing a Maximum Principle for Finite Horizon State Constrained Problems via Parametric Examples. Part 2: Problems with Bilateral State Constraints. (18th August 2021)

• Record Type: Journal Article
• Authors: Huong, Vu Thi; Yao, Jen-Chih; Yen, Nguyen Dong
• Is Part Of: Numerical functional analysis and optimization. Volume 42:Number 11(2021)
• Page Start: 1334
• Page End: 1366
• Publication Date: 2021-08-18
• Subjects: Borel measurable function -- function of bounded variation -- finite horizon optimal control problem -- Lebesgue-Stieltjes integral -- maximum principle -- solution existence theorem -- state constraint; 49K15 -- 49J15; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2021.1959344
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In this article, a maximum principle for finite horizon state-constrained problems is analyzed via parametric examples. These parametric examples resemble typical optimal growth problems in mathematical economics. Since the maximum principle is only a necessary condition for local optimal processes, a large amount of additional investigations are needed to obtain a comprehensive synthesis of finitely many processes suspected for being local minimizers. Our analysis not only helps to understand the principle in depth, but also serves as a sample of applying it to meaningful prototypes of optimal economic growth models. Problems with unilateral state constraints have been studied in Part 1 of the article. Problems with bilateral state constraints are addressed in this Part 2.