those are indeed very popular tools but for a slightly different kind of problem than this package is attempting to solve

Yes, especially Highs is completely unrelated because it's for (mixed integer) linear programming problems and quadratic programming problems, so it's not able to solve the types of problems described in this manuscript.

IPOPT is a bit of a stretch but I do know that there are some people in the mathematical programming space that use IPOPT's constraint satisfaction piece for solving a nonlinear system in a pinch, but it's not the main use case of IPOPT which is nonlinear optimization with nonlinear (in)equality constraints. This case has no optimization and is just nonlinear equality constraints, which you can then specialize quite a bit on. But while it is considered common knowledge in numerical circles to not use a nonlinear optimizer to solve nonlinear systems, I don't have a good canonical benchmark to point to on that, so we might as well make this it.

Thank you very much for your answer!

IPOPT as mentioned in other posts solves Nonlinear Optimization Problems. Working around it to make it solve nonlinear equations or nonlinear least squares problems typically doesn't go well. We will add benchmarks for the NLLS part (which we don't talk about in the paper) and that will contain IPOPT comparisons.

For some comparison (this is not a benchmark me or anyone on this paper have written), see https://juliapackagecomparisons.github.io/comparisons/math/n.... Specialized solvers for NLLS pretty much always beat general optimization solvers.