  The paper concerns the study of criticality of Lagrange multipliers in
variational systems that has been recognized in both theoretical and numerical
aspects of optimization and variational analysis. In contrast to the previous
developments dealing with polyhedral KKT systems and the like, we now focus on
general nonpolyhedral systems that are associated, in particular, with problems
of conic programming. Developing a novel approach, which is mainly based on
advanced techniques and tools of second-order variational analysis and
generalized differentiation, allows us to overcome principal challenges of
nonpolyhedrality and to establish complete characterizations on noncritical
multipliers in such settings. The obtained results are illustrated by examples
from semidefinite programming.
