One-parameter families of optimization problems: equality constraints

The authors introduce generalized critical points and discuss their relationship with other concepts of critical points (resp., stationary points). Generalized critical points play an important role in parametric optimization. Under generic regularity conditions. They study the set of generalized critical points, in particular, the change of the Morse index. They focus their attention on problems with equality constraints only and provide an indication of how the present theory can be extended to problems with inequality constraints as well.