Retain the original OptimizationProblem in OptimizationCache (#1191)

[ChrisRackauckas-Claude]

Summary

Fixes (the Optimization.jl side of) #1191. An OptimizationSolution only carries the solved OptimizationCache in sol.cache. The cache's instantiated f bakes the parameters p into the objective/constraint closures (see OptimizationDIExt.jl, where cons_oop closes over p in a let f=f, p=p block), so the original problem is effectively unrecoverable from a solution. As the reporter notes, that forces a constrained OptimizationAdjoint in SciMLSensitivity to dig into those closures to recover the raw constraints/parameters — brittle.

This stores the original, untouched OptimizationProblem on the cache as a new prob field, so it is recoverable as sol.cache.prob.

What changed

• OptimizationCache gains a trailing prob::Pr field holding the as-constructed problem.
  • Dispatch-safe: every solver's __solve dispatches on the leading OptimizationCache{O}, and the only two-parameter method (isinplace) uses the leading parameters. Appending a trailing type parameter/field disturbs nothing (no fieldnames/ConstructionBase/@set/custom getproperty enumerates the layout). Aqua.test_unbound_args stays green because the field is typed with the new parameter (prob::Pr).
• Both positional inner-constructor call sites pass prob: the main keyword constructor (OptimizationBase) and the duplicated constructor in OptimizationPRIMA.
• OptimizationPRIMA bumps its OptimizationBase compat lower bound to 5.2 (its constructor now requires the new field) and bumps its own version.
• OptimizationBase 5.1.3 → 5.2.0.

reinit! still only mutates reinit_cache; cache.prob holds the as-constructed problem (use cache.u0/cache.p for current state), as documented on the field.

Companion

A separate SciMLBase PR adds sol.prob/SciMLBase.get_prob(sol) so the issue's literal sol.prob request returns the original problem (it reads sol.cache.prob). This PR is independently useful — sol.cache.prob works today with it.

Tests (run locally)

Added a testset in solve_internals_test.jl that routes a constrained problem through the real OptimizationCache and asserts sol.cache.prob === prob, that the stored problem exposes the raw, non-p-baked objective/constraints (sol.cache.prob.f.cons === consfun, distinct from sol.cache.f.cons), and that p/lcons/ucons are preserved. Verified locally:

• solve_internals_test.jl (full file): all testsets pass (incl. new 12-assertion set).
• LBFGSB end-to-end (init/solve! and solve): sol.cache.prob is the original problem.
• PRIMA COBYLA constrained end-to-end: exercises the duplicated PRIMA constructor.
• Aqua.test_unbound_args(OptimizationBase): passes.
• Runic-formatted.

🚧 Draft — please ignore until reviewed by @ChrisRackauckas.

[ChrisRackauckas-Claude]

Companion SciMLBase PR (adds sol.prob/get_prob on top of this): SciML/SciMLBase.jl#1367. The two are independent — sol.cache.prob works with this PR alone.

[ChrisRackauckas-Claude]

CI note: all four package test jobs actually pass their tests — test (OptimizationBase, 1.11) and test (OptimizationPRIMA, lts) are green, and the logs for the two red ones show OptimizationBase tests passed / OptimizationPRIMA tests passed followed by the job exiting 255 on error: could not lock config file ~/.gitconfig: File exists during post-job cleanup (a git-config lock race between concurrent jobs on the self-hosted runner). So the red is infra-only; the test phases are green, matching the local run (full OptimizationBase suite 751/751, PRIMA COBYLA constrained). Same gitconfig-lock flake explains the downstream reds.