pounce-qp

Sparse parametric active-set quadratic programming subproblem solver for POUNCE. The QP subproblem solver inside the active-set SQP NLP path (Phase 5b) and the corrector inside pounce-sensitivity (Phase 5c).

Pure Rust, no FFI. Layered on pounce-common + pounce-linalg + pounce-linsol; tests use pounce-feral as the LDLᵀ backend.

Status

Phase 5a — feature-complete on correctness. Every problem class identified in the design note (dev-notes/research/active-set-sqp-warm-start.md) solves end-to-end; infeasibility is certified honestly; warm-start is wired. Five of the six analytical-ladder problems (§8.0) pass; problem #4 (LICQ-violating redundant equality) is a documented limitation that needs rank-detection beyond inertia control.

Phase 5a.1 — performance and tooling refinements landed. The Harris-style two-pass ratio test (cycling-prevention core of GMSW EXPAND), the QPS RANGES section, the cached-factor resolve infrastructure (the building block on which full Schur layers), and basic §8.2 scaling-sweep diagnostics all ship.

Phase 5a.2 — algorithmic completion landed. §4.2 sparse Schur-complement active-set updates (c18 standalone module + c19 wired into solve_general behind use_schur_updates) and §4.4 full GMSW EXPAND with τ-growth + snap-reset (c20) are both done. The Schur path is opt-in; correctness verified by Schur- vs-refactor cross-checks. EXPAND degrades to Harris-only behavior on non-cycling problems and only kicks in on pathological degeneracy. The remaining items (Maros-Mészáros oracle comparison, large-n scaling benchmarks) require FFI or benchmark infrastructure that fall outside the pure-Rust constraint.

Phase 5b — SQP NLP integration core landed in pounce-algorithm::sqp. The crate is now wired into the SqpAlgorithm outer loop via ParametricActiveSetSolver; SQP consumes any IpoptNlp and converges on convex equality NLPs (1 iter) and nonlinear NLPs (l1-merit line search, demonstrated on a circle-projection problem). AlgorithmBuilder exposes the SQP path via algorithm = ActiveSetSqp and the sister build_sqp_with_backend method.

What works

Problem class	Path	Tested
Unconstrained QP	`solve_equality_only` fast path (m=0, no bounds)	ladder #1
Equality-only (free vars)	`solve_equality_only`	ladder #2
Box-constrained (m=0)	`solve_box_constrained`	ladder #3
Equality + bounds (bound-feasible eq solution)	`solve_equality_plus_bounds`	dedicated tests
General inequalities (cold-feasible)	`solve_general`	dedicated tests
Warm-start with arbitrary working set	`solve_general`	drop / one-iter tests
Bound- or inequality-infeasible cold start	`solve_elastic` (l1-elastic mode, §4.3)	dedicated tests
Certified infeasibility detection	`solve_elastic` + `is_feasible` check	ladder #5
Indefinite H with PD reduced Hessian	inertia-controlled factor (§4.5)	ladder #6
Indefinite H requiring shift	`factorize_with_inertia_control` retry loop	dedicated test

Algorithmic feature	Status
Sparse triplet KKT assembly over `SymTMatrix` / `GenTMatrix`	done
§4.5 inertia control via diagonal-shift retry	done
§4.3 l1-elastic mode	done
§4.7 iterative refinement (inherited from FERAL)	done
§4.4 anti-cycling: Bland's rule (`AntiCyclingChoice::Bland`)	done (c8)
§4.4 anti-cycling: Harris two-pass (`AntiCyclingChoice::Expand`)	done (c14)
§4.4 anti-cycling: full GMSW EXPAND (τ-growth + snap-reset)	done (c20)
§4.2 cached-factor `resolve` infrastructure	done (c16)
§4.2 sparse Schur-complement update standalone (`schur::SchurState`)	done (c18)
§4.2 sparse Schur wired into `solve_general` (`use_schur_updates`)	done (c19)
§8.1 Maros-Mészáros .qps reader (incl. RANGES)	done (c11, c13)
§8.1 Maros-Mészáros oracle comparison (qpOASES / OSQP)	deferred (FFI; not pure-Rust)
§8.2 basic scaling-sweep diagnostics	done (c15)
§8.2 large-n scaling (LASSO at 10²–10⁵, MPC horizon 10–160)	Phase 5a.2
§8.7 per-module unit tests for `kkt`, `elastic`, `refinement`, `qps`	done

Public API at a glance

use pounce_qp::{ParametricActiveSetSolver, QpProblem, QpSolver, QpOptions, QpWarmStart};
use pounce_feral::FeralSolverInterface;

let mut solver = ParametricActiveSetSolver::new(Box::new(FeralSolverInterface::new()));
let sol = solver.solve(&qp, Some(&ws), &QpOptions::default())?;
assert_eq!(sol.status, pounce_qp::QpStatus::Optimal);

For the QPS / Maros-Mészáros on-ramp:

use pounce_qp::parse_qps;
let model = parse_qps(qps_text)?;
// ... wrap model.h_irow / model.a_irow / model.g / model.bl ... into
// pounce-linalg SymTMatrix / GenTMatrix and pass to solver.solve.

Tests

76 tests: 70 unit tests across 8 modules under src/tests/, plus 6 integration tests under tests/.

src/tests/analytical.rs (26) — §8.0 ladder + integration tests for every problem class, with hand-derived expected values.
src/tests/api.rs (11) — type-plumbing invariants for WorkingSet, QpProblem::validate, default QpOptions.
src/tests/kkt_unit.rs (5) — §8.7 unit tests for KktTriplet::add_h_diagonal_shift.
src/tests/elastic_unit.rs (7) — §8.7 unit tests for ElasticReformulation::build and initial_seed.
src/tests/refinement_unit.rs (4) — §4.7 pin that FERAL's iterative refinement is on by default and delivers near-machine-precision; plus c16 cached-resolve contract tests.
src/tests/qps_unit.rs (8) — QPS parser + round-trip solve + RANGES semantics for each row sense.
src/tests/scaling_unit.rs (3) — §8.2 scaling-sweep diagnostics at n ∈ {10, 50, 100, 200} and a warm-restart speedup test (cold: ~30 refactors / ~20 ws changes; warm at optimum: 1 refactor / 0 ws changes — the §8.5 payoff in microcosm).
src/tests/schur_unit.rs (6) — Schur-complement update unit tests.
tests/ (6) — cold_general_initial_regression.rs and mm_published_optima.rs integration regressions.

Run with: cargo test -p pounce-qp. For per-test timings, cargo test -p pounce-qp --release -- --nocapture.

Design reference