The paper is concerned with a class of quasidifferentiable functions in the sense of \textit{V. F. Demyanov} and \textit{A. M. Rubinov} [Dokl. Akad. Nauk SSSR 250, 21-25 (Russian) (1980; Zbl 0456.49016)]. Such functions are directionally differentiable and their directional derivatives are representable as a difference of two sublinear functions. By a dual correspondence with a quasidifferentiable function f is associated a class of pairs of convex compact sets called the quasi-differential of f at a point x. The calculus of such quasidifferentials is briefly introduced in the paper and an optimization problem subject to quasidifferentiable equality and inequality constraints is studied. Optimality conditions for this problem are given in terms of quasidifferentials in the form of set inclusions. This refines and simplifies the results of \textit{V. F. Demyanov}, \textit{L. N. Polyakova} and co-workers [U.S.S.R. Comput. Math. Math. Phys. 20, No.4, 34-43 (1980; Zbl 0466.90068); Vestn. Leningr. Univ. 1982, No.7, Mat. Mekh. Astron. No.2, 75-80 (Russian. English summary) (1982; Zbl 0488.90061); Kibernetika 1982, No.2, 119-122 (Russian. English summary) (1982; Zbl 0526.49015)].