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 = partial derivativeF/partial derivativey, 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. (C) 2002 Elsevier Science Ltd. All rights reserved.
local optimization data perturbations set filtration global optimization