Bifurcation Analysis for Perturbations of the First-Order Conditions of Optimality

The primary purpose of this work is to analyze the structure and persistence of critical point solutions of smooth perturbations of the Fritz John necessary conditions of optimality. These perturbations arise in the parametric techniques for solving constrained problems such as the quadratic penalty, the logarithmic-barrier functions, and the multiplier methods. The analysis is started with the formulation of the Fritz John conditions as algebraic system of equations. The singularities of this system are then classified and solutions are investigated at each type of singularity of codimension zero and one in terms of the bifurcation behavior of the curve of critical points.