I have a system of nonlinear equations of which I know it has a single root I am interested in, and has a continuum of roots I am not interested in. I am currently using Newton with line-searching in an attempt to find that single root, but the algorithm will obviously always converge to one of the roots from the continuum, as there are infinity of them.
How should I go about excluding such roots from my system of equations?
My first idea was to add sharp Gaussian functions to my system of equations that are non-zero at those roots, and almost zero everywhere else. I am currently implementing this, but it already seems like convergence is now very slow and inconsistent.
Would I be better off rewriting my problem as an optimization problem? I would have to find a global minimum of a constrained function.