Lack of Equality between Abel and Cesaro Limits in Discrete Optimal Control and the Implied Duality Gap

Abstract: In a paper it has been shown that if Cesaro and Abel limits for a certain discrete time optimal control problem are not equal, then there is a duality gap between a certain infinite-dimensional linear programming problem and its dual. In this paper we construct an example of a problem satisfying the assumptions of the aforementioned paper, where Cesaro and Abel limits are different.