Presolve and multistart

Presolve

result = pympcc.solve(problem, strategy="scholtes", presolve=True)

Two passes run when presolve=True:

1. Pinned-variable elimination — variables with xl[j] == xu[j] are substituted out of the optimisation; results are auto-expanded back to the original variable space.

2. Linear FBBT — feasibility-based bound tightening on rows detected as linear by a single bounded perturbation. Up to 50 fixed-point sweeps; detected infeasibility falls back to the identity map and emits a UserWarning.

When nothing can be eliminated, the presolve is a no-op.

For finer control:

from pympcc import presolve

reduced_problem, pmap = presolve(problem)
result = pympcc.solve(reduced_problem)
expanded_x = pmap.expand(result.x)   # back to original n

Multistart

ms = pympcc.multistart(
    problem,
    n_starts=20,
    perturb_scale=0.5,
    seed=0,
    strategy="scholtes",     # forwarded as solve_kwargs
)

ms.best         # MPCCResult — best run by objective among successes
ms.runs         # list[MPCCResult] — every start

Useful when the MPCC has multiple stationary points (typical for bilevel and equilibrium models). Each start perturbs x0 by perturb_scale * randn(n). Currently sequential; parallel n_jobs is on the roadmap (§6.1).