Constraints Optimal Control Problem for Quaternary Nonlinear Elliptic System

Abstract

This paper is concerned with the study of the constraints quaternary continuous classical optimal control vector problem (CQCCOCVP) with equality and inequality constraint controlled by quaternary nonlinear elliptic partial differential equations (QNLEPDEqs).The existence theorem of a CQCCOCV of the constrained problem is stated and proved under suitable hypotheses. The mathematical formulation of the adjoint quaternary equations (AQEqs) associated with the QNLEPDEqs is derived, the Fréchet derivative for the objective function and the EINC are derived. Finally, the necessary condition theorem and the sufficient condition theorem for the optimality are stated and proved.