Structure of Pareto sets in multiple objective Markov Decision Processes

First of all, I intend to remind us of several properties of

polyhedral cones and cone-generated orders which will be used for constructing Pareto sets in multiple objective optimisation problems.

Afterwards, I will consider multiple objective discounted Markov Decision Process. Methods of Convex Analysis and the Dynamic Programming Approach allow one to construct the Pareto sets and study their properties. For instance, I will show that in the unichain case, Pareto sets for different initial distributions are topologically equivalent. Finally, I will present an example on the optimal management of a deteriorating system.