Bifurcation Theorems via Second-Order Optimality Conditions1

We present a new approach to bifurcation study that relies on the theory of second-order optimality conditions for abnormal constrained optimization problems developed earlier by the first author.This theory does not subsume the “primal” description of the feasible set in terms of tangent vectors or in any other way.As a result, we obtain new sufficient conditions for bifurcation, which are to some extent complementary with respect to the known bifurcation theory