Full Optimizer approach for MOI interface

[sshin23]

With this approach,

using PowerModels, NLPModelsIpopt, ExaModels

@time pm = PowerModels.instantiate_model(
    joinpath(ENV["PGLIB_DEPOT"], "pglib_opf_case1354_pegase.m"),
    ACPPowerModel,
    PowerModels.build_opf
)
@time optimize_model!(
    pm,
    optimizer= ()->ExaModels.Optimizer(
        ipopt;
        linear_solver="ma27"
    )
)

and

using PowerModels, ExaModels, MadNLP, MadNLPHSL, MadNLPGPU, CUDA

@time pm = PowerModels.instantiate_model(
    joinpath(ENV["PGLIB_DEPOT"], "pglib_opf_case1354_pegase.m"),
    ACPPowerModel,
    PowerModels.build_opf
)
@time optimize_model!(
    pm,
    optimizer= ()->ExaModels.Optimizer(
        madnlp, CUDABackend()
    )
)

should work, though CUDA will complain that you're performing scalar indexing for the CUDA array (happening in non performance-critical part), which can be fixed in the future.

I'm not sure yet if the full optimizer approach would be the right approach here.

Upsides

• If we create an Optimizer, we can directly handle the interface with the solvers, so it will make interfacing with GPU-accelerated solvers (MadNLP) easier.

Downsides

• For each solver, extension packages need to be implemented ExaModelsIpopt, ExaModelsMadNLP, etc., which will eventually make the maintenance more difficult.

Thoughts? @odow @frapac @ccoffrin

[odow]

Not immediately obvious to me: does this exploit the repeated structure? Or does it create N independent constraints?

[sshin23]

@odow It does exploit the repeated structure. It first goes into each scalar term, and create expression tree and the associated data entry. If the expression tree is redundant (something we already have created), it doesn't store it, and just add a new data entry to the data array associated with that expression tree.

Compared to native ExaModels API, there is significant overhead when creating the model (as we need to inspect each scalar term), but the AD performance is pretty close to native ExaModels API.

[odow]

Ah cool! Okay. It should be possible then to make this an AD backend as well. That'd enable a fairer comparison.

[sshin23]

One caveat though, is that we don't have interface to MOI.Nonlinear yet. We only have an interface to MOIU.CachingOptimizer's expression tree. Thus, to make this as a MOI.AutomatidDifferentiationBackend, there should be some interface from JuMP that allows you to directly use MOIU.CachingOptimizer instead of hadling them via MOI.Nonlinear

[odow]

Yeah I was imagining repurposing your code for the Expr case, rather than directly trying to use this. I just couldn't figure out how to build scalar expressions and detect if they were the same using your framework when I tried a couple of weeks ago.

[sshin23]

@odow This is the approach taken in ExaModels.jl
https://github.com/exanauts/ExaModels.jl/blob/main/ext/ExaModelsMOI.jl#L28-L53

We build this nested Bin, which stores expression tree in head and stores data entries in data.