This text deals with the construction of correct extensions of extremal problems including problems of multicriterial optimization and more general problems of optimization with respect to a cone. The methods of qualitative stability and asymptotically insensitive analysis proposed here are particularly applicable to problems of optimal control with integrally constrained openloop controls. A non-traditional mathematical tool using elements of finitely-additive measure theory is applied, which necessitated special research concerned with approximative analogues of the Radon-Nikodym property. These abstract constructions do, however, address the essence of the problem at hand, and may find other applications as well.
