Optimization of implicitly defined functions

Gradient methods for local optimization of implictly defined functions are presented. The methods are structurally unstable under data perturbations that create null-points of Fy = , where F(x,y) = 0 defines y(x). Then, a set filtration method for global optimization of implictly defined functions under constraints is proposed which is structurally stable under data perturbations. Example are considered illustrating theory and numerical algorithms.