Groupe d’études et de recherche en analyse des décisions

# An Approach to the Existence of Pareto Solutions for Vector Valued Infinite Horizon Optimal Control Problems

## Dean A. Carlson

Existence theorems for Pareto optimal solutions of infinite horizon optimal control problems, with cost criteria described by a vector valued improper integral, are obtained. Motivated by the analogous scalar case, we do not a priori assume that the components of the cost function converge. Thus we consider extensions of the weaker notions of optimality described in the works of Brock, Haurie, et al. By considering a partial order described by a convex cone, we replace the vector valued minimization problem by an equivalent nonsmooth Lagrange problem. This permits us to achieve our results by applying several recent scalar valued existence results due to the author.

, 25 pages