Google Ceres Solver solves robustified non-linear bounds constrained least squares problems.
Can I use a non-linear least squares solver to find the solutions of a system of non-linear equations?
From Wikipedia: "The method of least squares is a standard approach to the approximate solution of overdetermined systems, i.e., sets of equations in which there are more equations than unknowns."
Now, since a "normal" system of non-linear equations should be in the set of overdetermined systems (in the degenerate case where the number of unknowns is equal to the number of equations), can I deduce I can use a non-linear least squares solver for this purpose?
This question comes from the fact that I have to use the Google Ceres Solver library that only seems to provide methods for non-linear least squares.
References:
Ceres Solver tutorial
Non-linear least squares solver to solve a system of non-linear equations?
Yes. Just formulate it as if you want to minimize the sum squared norm of each equation. Of course there are always issues of convergence to a local minimum of the resulting optimization problem, but the only way to get around it is to come up with a decent initial guess of the solution.