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Add TrustRegion to the documentation #123

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Jan 18, 2023
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Add TrustRegion to the documentation #123

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dc78743
Add TrustRegion to the documentation
ChrisRackauckas Jan 18, 2023
203426c
update recommendation
ChrisRackauckas Jan 18, 2023
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1 change: 1 addition & 0 deletions docs/src/api/nonlinearsolve.md
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Expand Up @@ -6,4 +6,5 @@ These are the native solvers of NonlinearSolve.jl.

```@docs
NewtonRaphson
TrustRegion
```
8 changes: 5 additions & 3 deletions docs/src/solvers/NonlinearSystemSolvers.md
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Expand Up @@ -7,11 +7,11 @@ Solves for ``f(u)=0`` in the problem defined by `prob` using the algorithm

## Recommended Methods

`NewtonRaphson` is a good choice for most problems. For large
`TrustRegion` is a good choice for most problems. For large
systems, it can make use of sparsity patterns for sparse automatic differentiation
and sparse linear solving of very large systems. That said, as a classic Newton
method, its stability region can be smaller than other methods. Meanwhile,
`SimpleNewtonRaphson` and `TrustRegion` are implementations which are specialized for
`SimpleNewtonRaphson` and `SimpleTrustRegion` are implementations which are specialized for
small equations. It is non-allocating on static arrays and thus really well-optimized
for small systems, thus usually outperforming the other methods when such types are
used for `u0`. `DynamicSS` can be a good choice for high stability.
Expand All @@ -36,6 +36,8 @@ features, but have a bit of overhead on very small problems.

- `NewtonRaphson()`:A Newton-Raphson method with swappable nonlinear solvers and autodiff
methods for high performance on large and sparse systems.
- `TrustRegion()`: A Newton Trust Region dogleg method with swappable nonlinear solvers and
autodiff methods for high performance on large and sparse systems.

### SimpleNonlinearSolve.jl

Expand All @@ -48,7 +50,7 @@ methods excel at small problems and problems defined with static arrays.
- `Klement()`: A quasi-Newton method due to Klement. It's supposed to be more efficient
than Broyden's method, and it seems to be in the cases that have been tried but more
benchmarking is required.
- `TrustRegion()`: A dogleg trust-region Newton method. Improved globalizing stability
- `SimpleTrustRegion()`: A dogleg trust-region Newton method. Improved globalizing stability
for more robust fitting over basic Newton methods, though potentially with a cost.

!!! note
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