A Pareto–Pontryagin Maximum Principle for Optimal Control

In this paper, an attempt to unify two important lines of thought in applied optimization is proposed. We wish integrate the well-known (dynamic) theory Pontryagin optimal control with Pareto (of static type), involving maximization/minimization a non-trivial number functions or functionals, offers definitive theoretical device for dynamic realization objectives be optimized. The undoubtedly less known mathematical literature, even if it was studied topological and variational details (Morse theory) by Stephen Smale. This reunification, obviously partial, presents new conceptual problems; therefore, basic review necessary desirable. After review, we define theories. Finally, propose extension recent multiobjective application evolution trees related anatomy xylems. work intended as first contribution series developed authors on subject.