Value Functions and Optimality Conditions for Nonconvex Variational Problems with an Infinite Horizon in Banach Spaces

• 成果类型: Article
• 署名作者: Frankowska, Helene; Sagara, Nobusumi
• 署名单位: Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite; Hosei University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2021.1130
• 发表日期: 2022
• 页码: 320-340
• 关键词: continuous-time model; VISCOSITY SOLUTIONS; transversality conditions; MAXIMUM PRINCIPLE; euler-lagrange; optimal-growth; DUALITY-THEORY; calculus

摘要

We investigate the value function of an infinite horizon variational problem in the infinite-dimensional setting. First, we provide an upper estimate of its Dini-Hadamard subdifferential in terms of the Clarke subdifferential of the Lipschitz continuous integrand and the Clarke normal cone to the graph of the set-valued mapping describing dynamics. Second, we derive a necessary condition for optimality in the form of an adjoint inclusion that grasps a connection between the Euler-Lagrange condition and the maximum principle. The main results are applied to the derivation of the necessary optimality condition of the spatial Ramsey growth model.