Use the default OptimizationCache in OptimizationIpopt

[SebastianM-C]

Summary

Cleans up OptimizationIpopt, which had copied OptimizationMOI's structure when it was created. The bespoke IpoptCache (a merge of MOI's MOIOptimizationNLPEvaluator + MOIOptimizationNLPCache) is replaced with OptimizationBase's default OptimizationCache, following the structure of OptimizationMadNLP: the package now only defines IpoptOptimizer, the SciMLBase traits, and __solve(::OptimizationCache{<:IpoptOptimizer}). Solver-specific state (derivative buffers, sparsity, call counters) lives in a transient IpoptEvaluator built inside __solve.

Deleted along with the custom cache: the hand-rolled __init, the ReInitCache getproperty delegation, the four solution accessors, the AutoSymbolics instantiation special-case (traits + the evaluator's lag_h → hess + cons_h fallback cover it), and dead MOI leftovers (int, obj_expr/cons_expr, a discarded sys, stale evaluator.J/evaluator.H comments).

Behavior fixes

• MaxSense sign bug: the evaluators negated f/grad/hess but __solve reported obj_val without flipping it back, so sol.objective (and the objective passed to user callbacks) had the wrong sign for maximization. Now handled with Ipopt's obj_scaling_factor = -1 (negative ⇒ maximize, unscaled objective reported), deleting all manual sign-flipping.
• reinit!(cache; p = ...) silently converged to the old optimum: the DI closures capture p at init time, so the objective saw the new parameters while every derivative saw the old ones. The evaluator now forwards the live cache.p (guarded for AutoSymbolics, NoAD without parameters, and p === nothing).
• Conditional second-order traits: requireshessian/requiresconshess/requireslagh (the latter was previously missing) now depend on hessian_approximation, so limited-memory runs skip Hessian AD generation entirely and pass eval_h = nothing to Ipopt. The unused cons_vjp is no longer generated — Ipopt's C API has no vjp/jvp callbacks.

Test suite

The three "automatically translated from the Ipopt tests" files were audited against the Ipopt repo; only two testsets actually traced back to it, both flawed:

• MyNLP was a different problem entirely — replaced with the real one (min −(x₂−2)² s.t. x₁² + x₂ − 1 = 0, optimum (±1, 0) with objective −4).
• LuksanVlcek1 had invented constraint bounds ([4,6] vs the registered [0,0]/[−1,0]) and a changed start — now the equality form with the original alternating start, pinned to its optimum.
• The restoration phase test's two equality constraints are mutually infeasible (on x₁²+x₂² = 0.5 the max of x₁³+x₂³ is ≈0.354 < 1), which is why its guarded assertion never ran; it now asserts ReturnCode.Infeasible.
• The warm-start test actually warm-starts via reinit!; print levels are verified through Ipopt's output_file; the option-priority test is now discriminating; the derivative test checks the derivative checker's verdict; stress-test RNGs are seeded.
• New tests: MaxSense objective/callback sign, reinit! with new parameters, limited-memory trait behavior.
• Pruned: redundant NLS/mixed-integer testsets, a non-smooth robust-optimization problem, a dead commented-out block, and a duplicate verbose loop. The inaccurate provenance headers are gone; EPL attribution stays on the genuinely Ipopt-derived problems (HS071, MyNLP, LuksanVlcek1).

MTK reinit! with new parameters remains @test_broken: the plain-vector form can't convert into the concretely typed ReInitCache{_, MTKParameters} field, and the symbolic-map form hits SciMLBase's generic process_p_u0_symbolic fallback ("Symbolic remake … is currently not supported"). Both need upstream fixes.

Test results (Julia 1.12.6, Pkg.test)

• Core: 125 passed, 0 failed, 1 broken (the documented MTK case)
• QA: 17 passed, 1 broken (pre-existing no_implicit_imports)

Version bumped to 1.3.0.

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