Necessary Conditions for Control Problems on Infinite Intervals Without Any Asymptotic Assumptions (Part 2)

In the second part of the talk, we will continue to examine control problems on infinite intervals with a weakly overtaking optimality criterion and the necessary boundary condition for such a formulation according to the maximum principle of L.S. Pontryagin, which serves as a transversality condition at infinity. The primary focus will be on the application of this boundary condition in various examples, thereby revealing the possibilities (or fundamental impossibilities) of certain simplifications. In particular, we will discuss the assumptions for the problem with a free right endpoint under which this condition is equivalent to the representation of the conjugate trajectory proposed by A.V. Kryazhimskiy and S.M. Aseev in the form of a Cauchy-type formula. At the end of the seminar, we plan to investigate a number of classical economic formulations based on this boundary condition.