ИСТИНА

For general constraint systems, we present the directional stability theorem based on the appropriate generalization of directional regularity condition. This theorem contains Robinson's stability theorem but does not reduce to it. Furthermore, we develop the related concept of directional metric regularity which is stable subject to small Lipschitzian perturbations of the constraint mapping, and which is equivalent to directional regularity for sufficiently smooth mappings. These results enable unification of some diverse ideas in optimization theory and variational analysis, and can serve as a basis for sensitivity analysis of variational and optimization problems, including MPECs. The latter are notorious for the lack of standard regularity of constraints, but can have directional regularity properties.