Abstract
This paper deals with the study of a new class of optimal control problems governed by nonlinear self-adjoint operator equations in Hilbert spaces under general constraints of the equality and inequality types on state variables. While the unconstrained version of such problems has been considered in our preceding publication, the presence of constraints significantly complicates the derivation of necessary optimality conditions. Developing a geometric approach based on multineedle control variations and finite-dimensional subspace extensions of unbounded self-adjoint operators, we establish necessary optimality conditions for the constrained control problems under considerations in an appropriate form of the Pontryagin Maximum Principle.