Necessary optimality conditions without a priori normality assumptions

In the linear space X with a given subset C⊂X set are the mappings F1: X→Rk 1, F2: X→Rk 2 and a function f: X→R1 (k1 and k2 are given). Considered is optimization problem: f(x)→min, x∈C, F1(x)≤0, F2(x)=0. For the considered rather general problem, the necessary first- and second-order extremum conditions are determined. The conditions are valid at introduced smoothness assumptions for Fi, f and closed C. The main difference of these conditions from the known is that though obtained without a priori normality assumptions (non-degeneracy of constraints) they remain informative (not degenerate). A typical example for such type of optimization problem, in which C is a convex closed cone, is the problem of optimal control with pulse controls.