How to choose a solver

The best choice of solver depends a lot on your problem! If you're not too sure which to pick, here is some guidance for what usually works well.

Tip

For advanced users: you can often adjust the behaviour of individual solvers, e.g. by using alternative line searches. Moreover you can also mix-and-match components to derive custom optimisers, see here.

Minimisation problems

For relatively "well-behaved" problems -- ones where the initial guess is likely quite close to the true minimum, and the function tends to look a bit like a bowl:

then the best choice is usually an algorithm like optimistix.BFGS or optimistix.NonlinearCG. By assuming that your function is relatively well-behaved, then these try to take larger steps to get the minimum faster.

For "messier" problems -- where the surface of the function is not so well-behaved -- then a first-order gradient algorithm often works well. These work by taking many small steps, and never moving too far away from the current best-so-far. The Optax library is dedicated to such algorithms; as such you should try e.g. optimistix.OptaxMinimiser(optax.adabelief(learning_rate=1e-3), rtol=1e-8, atol=1e-8).

Least-squares problems

These are an important special case of minimisation problems.

Either optimistix.LevenbergMarquardt or optimistix.Dogleg are recommended for most problems.

If your problem is particularly messy, as discussed above, then use a first-order gradient algorithm, e.g. optimistix.OptaxMinimiser(optax.adabelief(...), ...). These are compatible with optimistix.least_squares.

Root-finding problems

For one-dimensional problems, use optimistix.Bisection.

For relatively "well-behaved" problems, then either optimistix.Newton or optimistix.Chord are recommended.

If your problem is a little bit messy, then try optimistix.LevenbergMarquardt or optimistix.Dogleg. (These are compatible with root-finding problems.)

If your problem is particularly messy, as discussed above, then use a first-order gradient algorithm, e.g. optimistix.OptaxMinimiser(optax.adabelief(...), ...). (These are also compatible with root-finding problems.)

Fixed-point problems

For these, follow the same advice as for root-finding problems.