JuliaSmoothOptimizers / JuliaSmoothOptimizers/RegularizedProblems.jl

Running and convergence issues with FH model

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Description

@MohamedLaghdafHABIBOULLAH, @dpo

When playing the [demo](https://github.com/JuliaSmoothOptimizers/RegularizedOptimization.jl/blob/master/examples/demo-fh.jl), `TR` converges almost surely.
However, running `R2N` alone almost never works with the following error :

`┌ Warning: Interrupted. Larger maxiters is needed. If you are using an integrator for non-stiff ODEs or an automatic switching algorithm (the default), you may want to consider using a method for stiff equations. See the solver pages for more details (e.g. https://docs.sciml.ai/DiffEqDocs/stable/solvers/ode_solve/#Stiff-Problems).
└ @ SciMLBase ~/.julia/packages/SciMLBase/Pma4a/src/integrator_interface.jl:589`
`ERROR: DimensionMismatch: array could not be broadcast to match destination`

To make `R2N` work on most runs we first need to run `TR`, then run `R2N` on the same problem (with no reset). `iR2N` with exact prox has the same behaviour and inexact prox often give $$\xi <<0 $$. When using `TR` before a run, both `R2N` and `iR2N` sometimes hit `maxIter = 10 000`.

`R2` never works even with a prior run of `TR`.

Maybe we can play with how we define parameters in`fh_model` [here](https://github.com/JuliaSmoothOptimizers/RegularizedProblems.jl/blob/main/src/fh_model.jl#L32).

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