Existence of Optimal Solutions for Control and Variational Problems with Recursive Objectives

Carlson has formulated an open question as to the precise connections between conditions on the recursive objective functions for an optimal control model used by Carlson (J. Optim. Theory Appl.66 (1990), 311-336) and a variational model for optimal growth in Becker et al. (J. Econ. Theory47 (1989), 76-100). A complete answer to his question is provided by the introduction of a new lower closure result.