## “Linear Programming Approach to Long Run Average Optimal Control: The Non-Ergodic Case”

Giovedì 31 Ottobre 2019, ore 12:15 - Aula-seminari 430 - Vladimir Gaitsgory (Macquarie University, Sydney, Australia)

Abstract

We will discuss an infinite dimensional linear programming (IDLP) problem, which along with its dual allow one to characterize the limit optimal values of the infinite time horizon optimal control (OC) problem with time discounting and time averaging criteria. One of the results that will be in the center of our discussion is that establishing that the Abel and Cesaro limits of the optimal value of the OC problem are bounded from above by the optimal value of the IDLP problem and from below by the optimal value of its dual, this implying, in particular, that the Abel and Cesaro limits exist and are equal if there is no duality gap. The novelty of our consideration is that it is focused on the general case, when the limit optimal values may depend on initial conditions of the system.

The talk is based on results that have been recently obtained in collaboration with V. Borkar and I. Shvartsman.