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WIP: Linesearch with parabolic model - #127

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WIP: Linesearch with parabolic model#127
vchuravy wants to merge 5 commits into
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vc/parabolic_linesearch

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SIAMFANLEquations uses a parabolic model to update lambda, but I am unsure if it is worth it.

It reduces lambda much more aggressivly

| N | lambda_simple | lambda_parabolic |
| 1 | 1.0 | 1.0 |
| 2 | 0.5 | 0.5 |
| 3 | 0.25 | 0.2128 |
| 4 | 0.125 | 0.021282 |

That series is not precise, it can also look like:

[ Info: Line search iteration 1: lambda = 1.0, residual norm = 0.0010630827842760644, previous residual norm = 1.1155384180309512e-5
[ Info: Line search iteration 2: lambda = 0.5, residual norm = 0.00026829974217547483, previous residual norm = 1.1155384180309512e-5
[ Info: Line search iteration 3: lambda = 0.21357076293991317, residual norm = 5.298022713273962e-5, previous residual norm = 1.1155384180309512e-5
[ Info: Line search iteration 4: lambda = 0.023500742842848255, residual norm = 1.1166928919610728e-5, previous residual norm = 1.1155384180309512e-5
[ Info: Line search iteration 5: lambda = 0.009746226497557957, residual norm = 1.1091975115950218e-5, previous residual norm = 1.1155384180309512e-5

On the simple rosenbrock example we need more iterations with the parabolic backtracking than basic.

vchuravy and others added 5 commits April 17, 2026 15:12
Co-authored-by: Hendrik Ranocha <ranocha@users.noreply.github.com>
Co-authored-by: Hendrik Ranocha <ranocha@users.noreply.github.com>
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Once the build has completed, you can preview your PR at this URL: https://NumericalMathematics.github.io/Ariadne.jl/previews/PR127/ in a couple of minutes.

Base automatically changed from vc/linesearch to main April 20, 2026 19:24
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