# American Institute of Mathematical Sciences

December  2018, 11(6): 1121-1141. doi: 10.3934/dcdss.2018064

## Infinite-horizon multiobjective optimal control problems for bounded processes

 CRED EA 7321 Université Panthéon-Assas Paris 2, 12, Place du Panthéon, Paris, France

* Corresponding author

Received  September 2016 Revised  September 2016 Published  June 2018

This paper studies multiobjective optimal control problems in the discrete time framework and in the infinite horizon case for bounded processes. The paper generalizes to the multiobjective case results obtained for single-objective optimal control problems in that framework. The dynamics are governed by difference equations. Necessary conditions of Pareto optimality are presented namely Pontryagin maximum principles in the strong form and in the weak form. Sufficient conditions are also provided. Other notions of Pareto optimality are defined when the infinite series do not necessarily converge and links with these unbounded cases are established.

Citation: Naïla Hayek. Infinite-horizon multiobjective optimal control problems for bounded processes. Discrete & Continuous Dynamical Systems - S, 2018, 11 (6) : 1121-1141. doi: 10.3934/dcdss.2018064
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