Examples

Each page below is an executable notebook — built and run by Sphinx on every docs build, so the outputs you see are guaranteed to match the current code.

Getting started

• A first MPCC, walked through
• Tour of strategies
• MCP variable-paired form
• Sparse Jacobians
• Stationarity hierarchy: S / M / C / W
• KKT residual: how to read it

Notebook	Demonstrates
A first MPCC	The 15-line quickstart, walked through with full output explained.
Tour of strategies	Same problem solved by all six canonical reformulations.
MCP variable-paired form	comp_var_pairs for \(x_j \ge 0\ \perp\ F(x) \ge 0\) pairs.
Sparse Jacobians	COO sparsity for comp_G_jacobian, etc.; dense vs. sparse parity.
Stationarity hierarchy	S / M / C / W stationarity in one notebook.
KKT residual	Reading and recomputing result.kkt_residual.

Strategies & solvers

• Slack-lifting strategy
• NCP-function variants
• Multistart
• Stateful warm hot-start

Notebook	Demonstrates
Slack-lifting strategy	strategy="slack" for large-n MPCCs with dense \(G\), \(H\).
NCP variants	The seven smooth-NCP-function reformulations side-by-side.
Multistart	pympcc.multistart with n_starts, unique_optima(), parallel notes.
Stateful warm hot-start	MPCCSolver.resolve() for MPC and parametric sweeps.

Diagnostics & certification

• Presolve
• Diagnostics tour
• TNLP refinement

Notebook	Demonstrates
Presolve	Pinned-variable elimination, FBBT, dead-pair pruning.
Diagnostics tour	CQ, B-stationarity, SOSC, merit cross-check, degeneracy report.
TNLP refinement	Certified MPCC multipliers via tnlp_refine=True.

Bilevel & differentiable

• Bilevel KKT emission
• Differentiable solve with jax.grad
• Parametric sweep with pympcc.sensitivity

Notebook	Demonstrates
Bilevel KKT emission	pympcc.bilevel.from_lower_level on two small bilevels.
Differentiable solve	jax.grad through a converged MPCC; FD verification.
Parametric sweep	pympcc.sensitivity validated against a re-solve.