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.