[kxyvr]

Yes, care must be taken to stabilize the algorithm. However, I do not believe it to be true that no digits of accuracy can be obtained. The algorithm falls back to the Cauchy (steepest-descent) point on the first iteration and this will give reduction. That said, I'm willing to solve this particular problem and see. Where's your code for the DFN battery model? The page here leads to a dead github link:

https://help.juliahub.com/batteries/stable/api/#JuliaSimBatt...

[ChrisRackauckas]

The full DFN has a lot more going on. Use the benchmark-ified version from the benchmarks:

https://docs.sciml.ai/SciMLBenchmarksOutput/dev/NonlinearPro...

But as Avik states, this same kind of thing is done as part of the trust region methods, and so the trust region stuff with some ways to avoid J'J is effectively doing the same thing, though of course that cannot target a symmetric linear solver because J is not generally symmetric and it needs to do the L2 solve so it needs a QR/GMRES.

But indeed, let's get IPOPT in this interface and benchmarks and show it in the plots.

[kxyvr]

What's your convergence metric? It looks like x_sol gives a residual on the order of 1e-7. That's fine, but I'd like to measure an equivalent number to the benchmark.