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

2018/01/01 by Frankowska, Hélène, Sagara, Nobusumi
#49J50 #49J52 #49K15 #90C39 #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Control (math.OC) #Primary: 34A60 #Secondary: 49J53

paper · doi:10.48550/arxiv.1801.00400

Abstract

We investigate the value function of an infinite horizon variational problem in the infinite-dimensional setting. Firstly, 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. Secondly, 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.

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