Optimal control problems involving optimal economic growth with infinite horizon

摘要

We examine the existence of optimal solutions for a very general optimal economic growth problem with unbounded planning time horizon. A convexity hypothesis about a certain orientor field plays a crucial role in the proof. Then we conduct sensitivity analysis and determine the relation between optimal pairs and the initial capital accumulation. Finally we see what happens if the convexity hypothesis we have made no longer exists. This leads us to the introduction of the relaxed system and its comparison with the original one.