Solvers

DiffAPQP accepts continuous affine-parametric quadratic and linear programs and uses CVXPY solver interfaces for the forward pass. The default forward solver is OSQP. Linear programs are included in the QP rows below as the special case \(P=0\).

Default solver arguments

The following are DiffAPQP defaults, not necessarily the upstream defaults of each solver. They are applied by both SolMapLayer and ValueFuncLayer before each forward solve.

Solver	Backend form	Algorithm	DiffAPQP default solver_args
OSQP	QP	ADMM operator splitting	eps_abs=1e-5 eps_rel=1e-5 max_iter=100000
Gurobi	QP	Automatic continuous optimizer selection	Threads=1 OptimalityTol=1e-8 FeasibilityTol=1e-8 BarConvTol=1e-8
SCS	Conic	Douglas-Rachford operator splitting	eps_abs=1e-6 eps_rel=1e-6 max_iters=10000
ECOS	Conic	Primal-dual interior point	abstol=1e-8 reltol=1e-8 max_iters=200
Clarabel	Conic	Interior point with homogeneous embedding	tol_gap_abs=1e-8 tol_gap_rel=1e-8 max_iter=1000
QPALM	QP	Proximal augmented Lagrangian	eps_abs=1e-6 eps_rel=1e-6 max_iter=10000
PROXQP	QP	Primal-dual proximal augmented Lagrangian	eps_abs=1e-6 eps_rel=1e-6 max_iter=10000 backend="sparse"

For Gurobi, DiffAPQP does not set Method, so Gurobi selects the continuous optimization algorithm automatically. Threads=1 limits each individual solve to one solver thread; DiffAPQP can still solve different batch samples in parallel.

Overriding defaults

Values supplied in solver_args override the corresponding DiffAPQP defaults. Unspecified settings retain the values shown above:

primal_dict, *_ = layer(
    param_dict,
    solver="OSQP",
    solver_args={
        "eps_abs": 1e-7,
        "eps_rel": 1e-7,
        "max_iter": 200000,
    },
)

For a CVXPY-compatible solver without an explicit DiffAPQP profile, solver_args is empty and the solver uses its upstream defaults.

Warm-start and update support

The custom CVXPY fork provides DiffAPQP's sample-indexed warm-start and in-place data-update paths for OSQP, SCS, QPALM, and PROXQP. Other solvers use their standard CVXPY interfaces. See Installation for solver packages and custom-fork setup.

These settings apply only to the forward optimization solver. The solution-map layer's full-KKT or reduced-KKT adjoint method is configured separately through reduced_kkt, mode, and mode_args.