The design of sophisticated engineering systems (like the ship, airborne vehicle, production complex, etc.) is usually a multilevel process when the object under design is split up into separate sub-systems. At the same time, the quest for the best solutions for separate sub-systems should comply with requirements for optimality of the designed object as a whole. It is suggested to meet this condition with the help of local criteria developed using dual assessments (Lagrangian coefficients) of the duality theory in the non-linear mathematic programming. Application of the said criteria for the practical tasks has been reviewed.