slsqp_jax.slsqp.hvp

Lagrangian Hessian-vector product factories — L-BFGS-backed and exact (obj_hvp_fn + constraint HVP contributions).

slsqp_jax.slsqp.hvp

Lagrangian Hessian-vector product factories.

The QP subproblem needs v -> B v where B is some positive-definite approximation to the Lagrangian Hessian. Two strategies are supported:

  • Frozen L-BFGS (default): the L-BFGS history at the start of the SLSQP step is treated as constant for the duration of the inner CG loop. v -> B_k v is implemented via the compact representation in slsqp_jax.hessian.lbfgs_hvp().

  • Newton-CG (QPConfig.use_exact_hvp_in_qp = True): the exact Lagrangian HVP at the current iterate is used directly inside the CG loop. Each CG step costs one forward-over-reverse AD pass; on ill-conditioned problems this dramatically accelerates convergence.

The L-BFGS history is still updated regardless of which mode is active, because (a) it is the canonical source for the preconditioner and (b) it is the fallback in case a future revision skips an exact HVP evaluation.

slsqp_jax.slsqp.hvp.build_exact_lagrangian_hvp(*, fn, y, args, multipliers_eq, multipliers_ineq, obj_hvp_impl, eq_hvp_contrib_impl, ineq_hvp_contrib_impl, n_ineq_general)[source]

Build the exact Lagrangian HVP at the current iterate.

H_L v = H_f v − Σ λ_i H_{c_eq_i} v − Σ μ_j H_{c_ineq_j} v. The dispatch to user-supplied vs AD-computed contribution callables is resolved upstream in slsqp_jax.slsqp.derivatives.make_derivative_closures().

Return type:

Callable[[Float[Array, 'n']], Float[Array, 'n']]

Parameters:

  • fn (Callable)

  • y (Float[Array, 'n'])

  • args (Any)

  • multipliers_eq (Float[Array, 'm_eq'])

  • multipliers_ineq (Float[Array, 'm_ineq'])

  • obj_hvp_impl (Callable | None)

  • eq_hvp_contrib_impl (Callable)

  • ineq_hvp_contrib_impl (Callable)

  • n_ineq_general (int)

slsqp_jax.slsqp.hvp.build_lbfgs_lagrangian_hvp(lbfgs_history)[source]

Closure over the frozen L-BFGS history.

Return type:

Callable[[Float[Array, 'n']], Float[Array, 'n']]

Parameters:

lbfgs_history (LBFGSHistory)