2019/01/25 by Vũ Thị Thu Hương, Huong, Vu Thi, Jen‐Chih Yao +3
Economics, Econometrics and Finance · #49J15 #49K15 #Economic Growth and Productivity #Economic theories and models #FOS: Mathematics #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.1901.09718
openalex publication_date 2019/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the present paper, the maximum principle for finite horizon state constrained problems from the book by R. Vinter [Optimal Control, Birkhäuser, Boston, 2000; Theorem~9.3.1] is analyzed via parametric examples. The latter has origin in a recent paper by V.~Basco, P.~Cannarsa, and H.~Frankowska, and resembles the optimal growth problem in mathematical economics. The solution existence of these parametric examples is established by invoking Filippov's existence theorem for Mayer problems. Since the maximum principle is only a necessary condition for local optimal processes, a large amount of additional investigations is 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 economic optimal growth models. Problems with unilateral state constraints have been studied in Part 1 of the paper. Problems with bilateral state constraints are addressed in this Part 2.