Value Functions and Optimality Conditions for Nonconvex Variational Problems with an Infinite Horizon in Banach Spaces
研究了无限维空间中无限时域变分问题的值函数，给出了Dini-Hadamard次微分的上界估计，推导了伴随包含形式的最优性必要条件，并应用于空间Ramsey增长模型。
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.