On the existence of catching-up optimal solutions for Lagrange problems defined on unbounded intervals
We are concerned with the question of the existence of optimal solutions for infinite-horizon optimal control problems of Lagrange type. In such problems, the objective or cost functional is described by an improper integral. As dictated by applications arising in mathematical economics, we do not a priori assume that this improper integral converges. This leads us to consider a weaker type of optimality, known as catching up optimality. The results presented here utilize the classical convexity and seminormality conditions typically imposed in the existence theory for the case of finite intervals. These conditions are significantly weaker than those imposed by other authors; as a consequence, their existence results are contained as special cases of the results presented here. The method of proof utilizes the Carathéodory-Hamilton-Jacobi theory previously developed by the author for infinite-horizon optimal control problems.
infinite-horizon optimal control problems of Lagrange type
scientific article; zbMATH DE number 3915064