BatchExaModel: batch optimization with GPU support

[amontoison]

Summary

Adds BatchExaModel for solving multiple independent optimization instances that share identical structure but differ in parameter values. All instances share one compiled expression pattern and are fused into a single model for efficient SIMD/GPU evaluation.

Core features

• BatchExaCore(ns) — create a core for ns batch instances; variables, parameters, objectives, and constraints are defined once and replicated automatically
• Batch NLP API — obj!, grad!, cons!, jac_coord!, hess_coord! operate on matrix-valued (dim, ns) inputs
• FlattenNLPModel — wraps a BatchExaModel as a standard AbstractNLPModel{T, Vector{T}} for use with any NLPModels-compatible solver (e.g. Ipopt)
• get_model(model) — returns the solver-ready flat model for batch, identity for regular models
• var_indices(model, i) — extract per-instance solution from the flat solver output
• GPU support — batch KA kernels for obj, grad, cons, jac, hess; race-free obj kernel via fill+reduce
• Batched two-stage — TwoStageExaCore(ns; nbatch = Val(N)) combines batch and two-stage models

API additions

• BatchExaCore, BatchExaModel, FlattenNLPModel
• get_nbatch, get_model, var_indices, cons_block_indices
• @add_var, @add_par, @add_obj, @add_con, @add_con!, @add_expr all work with batch cores
• set_value! / get_value for updating parameters on the model (batch-aware, broadcasts across instances)
• set_parameter! deprecated in favor of set_value!

Other changes

• TwoStageExaCore / TwoStageExaModel with EachScenario() API, getter/setter helpers
• add_con consolidated to ns... varargs (single method handles both explicit dims and generator)
• append! fixed for N-dimensional arrays (fixes juliac COPSApp)
• build_extension widened from AbstractVector to AbstractArray so batch models get KA acceleration
• Pretty-print improvements: operator precedence parenthesization, bracket notation for integer indexing
• Benchmark noise reduction with minimum-based estimator

Tests

• BatchTest: construction, obj/grad/cons/jac/hess, bounds, error guards, Ipopt, set_value!, multidim vars, add_con!, add_expr, per-instance accessors, GPU backend loop
• TwoStageTest: construction, evaluation, Ipopt (inequality/equality/multi-var), batched two-stage (construction/eval/Ipopt), getters/setters
• GetterSetterTest: parameter/variable/constraint get/set API

Docs

• New docs/src/batch.jl tutorial with worked examples
• BatchNLPModels autodocs in API manual
• Updated docs/src/parameters.jl to use set_value!

cc @michel2323

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[amontoison]

@michel2323 Do you know how we can adapt the objective function to return a vector of nscenario instead of a scalar that is the sum of all objectives?
It is what we need for the new API of NLPModels.jl.

[michel2323]

Right. Forgot about the primal. How about the constraints?

I'll give it a try. Should be easy.

[amontoison]

For the constraints, we want to a strided API where the cosntraints of each scenarios are stored in the same vector.
It is like TwoStageExaModel and exactly what we do.

[michel2323]

For the objective, I've added the API below. This should be aligned with what be discussed back here.

    obj(model::TwoStageExaModel, x_global, s) → scalar

Evaluate the objective contribution of scenario s (for 1 ≤ s ≤ ns), or
the shared/design-only objective terms (for s = 0).

Per-scenario terms are Objective nodes whose iterator length is evenly divisible
by ns. Design-only terms (where length(itr) % ns != 0) are returned when s = 0.

The invariant obj(m, x) ≈ sum(obj(m, x, s) for s in 1:ns) + obj(m, x, 0) holds.

[michel2323]

We decided on a vectorized API obj(::BatchExaModel, x, result) where result is a vector of size ns.

[github-actions]

Benchmark Results