3 ms·

I dont know much about this but the fact that they did not mention IPOPT or Highs (which I would think them as two of the most popular software used for these p

I dont know much about this but the fact that they did not mention IPOPT or Highs (which I would think them as two of the most popular software used for these problems) made me question this too.

affinepplan 3y ago
those are indeed very popular tools but for a slightly different kind of problem than this package is attempting to solve
- ChrisRackauckas 3y ago
  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.
  - akutlay 3y ago
    Thank you very much for your answer!
avikpal1410 3y ago
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/nonlinear_solvers/index.html#performance_evaluation https://juliapackagecomparisons.github.io/comparisons/math/n.... Specialized solvers for NLLS pretty much always beat general optimization solvers.

I dont know much about this but the fact that they did not mention IPOPT or Highs (which I would think them as two of the most popular software used for these problems) made me question this too.

affinepplan 3y ago

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

ChrisRackauckas 3y ago
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.
- akutlay 3y ago
  Thank you very much for your answer!

avikpal1410 3y ago

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/nonlinear_solvers/index.html#performance_evaluation https://juliapackagecomparisons.github.io/comparisons/math/n.... Specialized solvers for NLLS pretty much always beat general optimization solvers.