Bifurcation analysis for perturbations of the first-order conditions of optimality (Q1343977)

The author studies the behavior of critical points of nonlinear programming problems under smooth perturbations. First, the Fritz-John necessary optimality conditions are rewritten as a system of nonlinear equations in the primal and dual variables. Then singularities of a general parameterized nonlinear system are classified and solutions to the perturbed nonlinear system with singularities of co-dimension zero and one are characterized. These results are then applied to the nonlinear system corresponding to the Fritz-John necessary optimality conditions.