Coexhasuters are families of convex compact sets allowing one to represent the approximation of the increment of the studied function in the neighborhood of a considered point in the form of MaxMin or MinMax of affine functions. Researchers developed a calculus of these objects, which makes it possible to build thesefamilies for a wide class of nonsmooth functions. They also described unconstrained optimality conditions in terms of coexhausters, which paved the way for the construction of new optimization algorithms. In this paper we derive constrained optimality conditions in terms of coexhausters.