API reference¶

Problem types¶

`MPCCProblem`	Defines an MPCC in the form.
`StructuredMPCC`	MPCC with explicitly separated linear and nonlinear constraint layers.
`ParametricMPCC`	JAX-traceable MPCC parameterised by an external vector `θ`.

Solving¶

`solve`	Solve an MPCC problem — convenience wrapper around `MPCCSolver`.
`MPCCSolver`	Solver for Mathematical Programs with Complementarity Constraints (MPCC).
`solve_jax`	Solve a parametric MPCC; returns `x*` differentiable in `θ`.
`multistart`	Solve problem from n_starts perturbed initial points.

Result types¶

`MPCCResult`	Result returned by `pympcc.solve()` or `pympcc.MPCCSolver.solve()`.
`IterationInfo`	Diagnostic snapshot for one NLP solve in an iterative strategy.
`IPOPTStatus`	IPOPT solver return codes (integer values match cyipopt's status field).
`MultiStartResult`	Aggregate result of a multi-start solve.
`TNLPResult`	Result of a TNLP active-set refinement re-solve (§2.6).
`SensitivityResult`	Result of a parametric sensitivity solve.

Diagnostics¶

`active_sets`	Partition constraint indices into active subsets at `result.x`.
`classify_cq`	Classify the strongest MPCC constraint qualification at `result.x`.
`degeneracy_report`	Combined degeneracy summary at `result.x`.
`initial_point_statistics`	Replicate PATH's `output_initial_point_statistics` at `x0`.
`jac_norms`	Row- and column-norm summary of the active-constraint Jacobian.
`merit_cross_check`	Cross-check three independent MPCC merit functions at `result.x`.
`sosc_check`	Check MPCC second-order sufficient conditions at `result.x`.
`classify_stationarity`	Classify the MPCC stationarity type of a solved result.
`compute_kkt_residual`	MPCC stationarity residual: `\|\|∇f + Jg^T λ_g + Jh^T λ_h + JG^T μ_G + JH^T μ_H - z_L + z_U\|\|_∞`.
`verify_b_stationarity`	Test B-stationarity of an MPCC solution by enumerating linearised-MPCC tangent-cone branches and solving an LP per branch.

Sensitivity¶

`sensitivity`	Compute `dx*/dp` via implicit differentiation through the KKT system.
`active_row_labels`	Return active-row labels in the order `sensitivity()` expects `dc_dp`.

Presolve and scaling¶

`presolve`	Reduce problem by FBBT, pinned-var elimination and dead-pair pruning.
`PresolveMap`	Mapping between an original `MPCCProblem` and its reduced form.
`autoscale_comp_pairs`	Return per-pair diagonal scales that equilibrate the comp block.
`unscale_multipliers`	Module-level alias for `MPCCResult.unscale_comp_multipliers()`.

Bilevel¶

bilevel.from_lower_level

Emit an MPCCProblem from a bilevel program.

I/O¶

frontend.ampl.from_nl

Read an AMPL text-format .nl file and return an pympcc.MPCCProblem.