Choosing a Solver

POUNCE is not a single solver but a small family of them sharing one numerical backbone. This page is the map: what each solver is, when to reach for it, and how they fit together.

The one-sentence version: convex and conic problems are solved to the global optimum; nonconvex problems are solved locally by default, or to a certified global optimum via the SOS (polynomial) and spatial branch-and-bound (general) paths. Every solver, whatever its flavor, ultimately factorizes a symmetric KKT system through the shared pounce-linsol layer, which in turn drives a pluggable backend (FERAL by default, HSL MA57 optionally).

The solvers at a glance

A general-purpose spatial branch-and-bound solver for factorable nonconvex NLPs (pounce-global) is in development on the feature/global branch and is not part of this release — there is no --solver global CLI route or minimize_global Python entry point yet. Today the only certified-global path for nonconvex problems is SOS / Lasserre, for polynomials.

When to choose each

General nonlinear program (the common case) → NLP filter-IPM

If your model has nonlinear objective or constraints and you don’t know (or can’t assume) convexity, this is the default and the most mature path. It is POUNCE’s port of Ipopt’s filter line-search interior-point method: robust on nonconvex problems, with a feasibility restoration phase for hard starts and exact or limited-memory Hessians. It returns a local KKT point — for a nonconvex problem there is no global guarantee.

• CLI: pounce model.nl (or a built-in problem).
• Python: the cyipopt-style Problem class, or the scipy-style minimize facade.
• Reach for limited-memory Hessians (hessian_approximation=limited-memory) when second derivatives are unavailable or expensive.

A sequence of related NLPs, or a stable active set → NLP active-set SQP

Selected with algorithm=active-set-sqp. It solves the NLP as a sequence of quadratic subproblems (handed to pounce-qp), which warm-starts extremely well when the active set is stable across solves — e.g. a parametric sweep or a control loop. For a single cold solve of a general NLP, prefer the filter-IPM.

Linear or convex quadratic program → Convex IPM (LP/QP)

If P ⪰ 0 (or P = 0 for an LP), use the convex interior-point solver: it returns the global optimum, detects primal/dual infeasibility, and offers warm-starting, batched and multiple-RHS solving, a build-once / solve-many QpFactorization handle, and post-optimal sensitivity (QpSensitivity — the sIPOPT analog). The CLI’s auto routing classifies an .nl and sends LP/convex-QP problems here automatically.

• Python: pounce.qp.solve_qp (and solve_qp_batch, solve_qp_multi_rhs).

Second-order, exponential, or power cones → Convex IPM (conic)

The same convex solver handles conic programs: second-order cones, the exponential and power cones that express geometric programming, entropy / log-sum-exp, logistic models, and p-norm constraints, and the positive-semidefinite cone for small dense SDPs. Also global. This is the path to use when you can cast a nominally-nonconvex problem into a convex cone — you trade modeling effort for a global guarantee. (The PSD cone is self-scaled and runs on the symmetric driver; the exp/power cones run on the non-symmetric HSDE driver, so the two families can’t yet be mixed in one problem.)

A common special case routes here automatically: a convex quadratically-constrained QP (QCQP). When auto routing finds a convex-quadratic inequality ½xᵀHx + aᵀx + b ≤ 0 (H ⪰ 0), it reformulates each such constraint to one second-order cone (H = FᵀF) and sends the whole problem to the conic solver — no .cbf and no manual cone bookkeeping needed. This works from a .nl/Pyomo model on the CLI and from minimize() in Python (which probes each constraint’s Hessian and only routes when it can prove the feasible set is convex). See LP / QP Solver Routing.

• Python: pounce.qp.solve_socp(..., cones=[("exp", 3), ("pow", 0.5), ...]) for an explicit cone program, or just minimize(...) for a convex QCQP.
• CLI: a Conic Benchmark Format file, pounce model.cbf (see the CBLIB benchmark tier), or any convex-QCQP .nl under auto routing.

Nonconvex problem, global optimum required → SOS or spatial branch-and-bound

When the problem is genuinely nonconvex and a local optimum is not good enough, the shipped path to a certified global optimum is for polynomials:

• Polynomial objective/constraints → SOS / Lasserre (sos_minimize, or pounce.sos_minimize). A single semidefinite program certifies the global minimum (the largest γ with p − γ in the Putinar cone), and the global minimizers are recovered from the moment matrix — even multiple ones, via a facial-reduction step. Best for modest degree and dimension; the SDP grows with the relaxation order.

A general-purpose spatial branch-and-bound solver for factorable nonconvex problems (including exp/ln/trig) — pounce-global — is in development on the feature/global branch and is not part of this release.

See Global Optimization for the SOS path in depth.

Indefinite QP, or a QP inner-solver → Active-set QP

pounce-qp is a sparse parametric active-set solver that accepts an indefinite Hessian (via inertia control), with two-sided bounds and factorization-reuse across a homotopy. It is the engine behind the active-set SQP path, and is the right choice for MPC-style problems or any setting where you re-solve a slowly-changing QP many times. Use the convex IPM instead when P ⪰ 0 and you want a single robust solve with infeasibility certificates.

How to override the automatic routing

The CLI classifies each .nl problem and picks a solver, but you can force the choice:

pounce model.nl --solver auto          # default: classify, then route
pounce model.nl --solver nlp           # filter-IPM (or active-set-sqp via algorithm=)
pounce model.nl --solver lp-ipm        # convex LP interior-point
pounce model.nl --solver qp-ipm        # convex QP interior-point
pounce model.nl --solver socp          # conic interior-point (convex QCQP)
pounce model.nl --solver qp-active-set # active-set QP

(The CLI spelling of the option is solver_selection=<value>, e.g. pounce model.nl solver_selection=qp-ipm.)

See LP / QP Solver Routing for how classification works and when it falls back to the more general solver.

The shared backbone

Every interior-point and active-set solver above assembles a symmetric KKT system and factorizes it through pounce-linsol. That trait layer is backend-agnostic:

• FERAL (pounce-feral) — a pure-Rust sparse symmetric LDLᵀ factorization. The default; no external dependencies.
• HSL MA57 (pounce-hsl) — the well-known Harwell solver via libcoinhsl, enabled with the ma57 build feature for large or ill-conditioned systems.

Because the backend is pluggable, the same solver code runs on either without change.

Cross-cutting layers

These are not solvers you select, but stages and tools the solvers share:

• Presolve (pounce-presolve) — an optional front-end that tightens bounds (feasibility-based bound tightening), removes redundant rows, and repairs LICQ degeneracies before the solve.
• Restoration (pounce-restoration) — the feasibility-recovery phase the filter-IPM enters when a step cannot reduce both infeasibility and the objective; pounce-l1penalty offers an ℓ₁-exact penalty reformulation for degenerate / LICQ-violating problems.
• Sensitivity — pounce-sensitivity gives sIPOPT-style parametric steps and reduced Hessians for the NLP; QpSensitivity does the same for the convex QP. See Sensitivity Analysis.
• Cone library (pounce-convex) — nonnegative, second-order, exponential, power, and (for small dense problems) positive-semidefinite cones, so small SDPs solve as a convex class. The PSD cone cannot yet be mixed with the exponential/power cones in one problem (they use different drivers).
• Solve report — every path can emit the machine-readable pounce.solve-report/v1 JSON (status, iterations, residuals, timing). See JSON Solve Report.

Global vs. local — the honest summary

POUNCE settles a problem globally along two routes, and locally along one:

• Global by convexity — LP, convex QP, SOCP, and the exponential / power / PSD cone classes. Local is global, so a convex or conic reformulation buys the guarantee outright.
• Global by certificate (polynomials) — the SOS / Lasserre optimizer certifies the global minimum of a nonconvex polynomial from a single SDP; see Global Optimization.
• Local for general NLP — the filter-IPM and SQP paths converge to a KKT point, which for a nonconvex problem carries no global guarantee.

A general-purpose spatial branch-and-bound route for factorable nonconvex problems (pounce-global) is in development on the feature/global branch but not in this release.

Two practical levers for a “global” answer: modeling (cast as much as you can into the convex cone library) and, when that is not possible, the SOS / Lasserre optimizer for polynomials.