Pareto optimal control for mixed Neumann infinite-order parabolic system with state-control constraints

A distributed Pareto optimal control problem for an infinite order parabolic system is considered. The performance index has a vector form with two components in integral form. Constraints on controls and on states are imposed. To obtain optimality conditions for the Neumann problem, the generalization of the Dubovitskii–Milyutin theorem was applied.