Core API

Stable, re-exported at the top level of qpax. These functions forward to whichever backend you select with the backend keyword.

Solvers

qpax.solve_qp

solve_qp(Q: Array, q: Array, A: Array, b: Array, G: Array, h: Array, *, backend: str = 'i', **kwargs: Any) -> tuple

Solve a convex QP via primal-dual interior point.

Parameters:

Name	Type	Description	Default
Q	Array	(n, n) PSD cost matrix.	required
q	Array	(n,) linear cost.	required
A	Array	(m, n) equality constraint matrix.	required
b	Array	(m,) equality constraint RHS.	required
G	Array	(p, n) inequality constraint matrix.	required
h	Array	(p,) inequality constraint RHS.	required
backend	str	"e" for the explicit predictor-corrector PDIP (default), "i" for the implicit retraction-manifold PDIP.	'i'
**kwargs	Any	forwarded to the selected backend (e.g. solver_tol, max_iter, linear_solver).	{}

Returns:

Type	Description
tuple	Tuple (x, s, z, y, converged, iters).

qpax.solve_qp_primal

solve_qp_primal(Q: Array, q: Array, A: Array, b: Array, G: Array, h: Array, *, backend: str = 'i', **kwargs: Any) -> jax.Array

Solve a QP and return the primal solution x.

Differentiable via jax.custom_vjp; gradients flow through every QP parameter using the implicit function theorem on the relaxed KKT system.

Parameters:

Name	Type	Description	Default
Q	Array	(n, n) PSD cost matrix.	required
q	Array	(n,) linear cost.	required
A	Array	(m, n) equality constraint matrix.	required
b	Array	(m,) equality constraint RHS.	required
G	Array	(p, n) inequality constraint matrix.	required
h	Array	(p,) inequality constraint RHS.	required
backend	str	"e" for the explicit backend (default), "i" for the implicit backend.	'i'
**kwargs	Any	forwarded to the selected backend (e.g. solver_tol, target_kappa, max_iter).	{}

Returns:

Type	Description
Array	Primal solution x of shape (n,).

qpax.solve_qp_elastic

solve_qp_elastic(Q: Array, q: Array, G: Array, h: Array, penalty: float, *, backend: str = 'e', **kwargs: Any)

Solve the elastic QP relaxation of an inequality-constrained QP.

Parameters:

Name	Type	Description	Default
Q	Array	(n, n) PSD cost matrix.	required
q	Array	(n,) linear cost.	required
G	Array	(p, n) inequality constraint matrix.	required
h	Array	(p,) inequality constraint RHS.	required
penalty	float	per-unit cost of slack on each inequality.	required
backend	str	only "e" is supported; "i" raises NotImplementedError.	'e'
**kwargs	Any	forwarded to the explicit backend (e.g. solver_tol, max_iter).	{}

qpax.solve_qp_elastic_primal

solve_qp_elastic_primal(Q: Array, q: Array, G: Array, h: Array, penalty: float, *, backend: str = 'e', **kwargs: Any) -> jax.Array

Differentiable elastic-QP solve returning only the primal x.

Parameters:

Name	Type	Description	Default
Q	Array	(n, n) PSD cost matrix.	required
q	Array	(n,) linear cost.	required
G	Array	(p, n) inequality constraint matrix.	required
h	Array	(p,) inequality constraint RHS.	required
penalty	float	per-unit cost of slack on each inequality.	required
backend	str	only "e" is supported; "i" raises NotImplementedError.	'e'
**kwargs	Any	forwarded to the explicit backend.	{}

qpax.relax_qp

relax_qp(Q: Array, q: Array, A: Array, b: Array, G: Array, h: Array, x: Array, s: Array, z: Array, y: Array, *, backend: str = 'e', **kwargs: Any) -> tuple

Refine a PDIP solution to a relaxed (kappa-perturbed) KKT point.

Parameters:

Name	Type	Description	Default
Q	Array	(n, n) PSD cost matrix.	required
q	Array	(n,) linear cost.	required
A	Array	(m, n) equality constraint matrix.	required
b	Array	(m,) equality constraint RHS.	required
G	Array	(p, n) inequality constraint matrix.	required
h	Array	(p,) inequality constraint RHS.	required
x	Array	primal warm start, shape (n,).	required
s	Array	inequality slack warm start, shape (p,).	required
z	Array	inequality dual warm start, shape (p,).	required
y	Array	equality dual warm start, shape (m,).	required
backend	str	"e" for the explicit backend (default), "i" for the implicit backend.	'e'
**kwargs	Any	forwarded to the selected backend (e.g. solver_tol, target_kappa, max_iter).	{}

Returns:

Type	Description
tuple	Tuple (x, s, z, y, converged, iters) of the refined solution.

Types

qpax.QPData

Bases: NamedTuple

qpax.QPState

Bases: NamedTuple

qpax.SolverParams

Bases: NamedTuple

qpax.LinearSolver

Bases: Enum