Sparse derivative oracle

Initialize and evaluate the value, gradient, sparse constraint Jacobian and sparse Lagrangian Hessian of a problem built with sd_problem. Derivatives come in two forms, matching 'sparsediffpy': coordinate (COO) form, with the Hessian as its lower triangle (the form CVXPY uses), and compressed-sparse-row (CSR) form, with the full Hessian.

Usage

sd_init_derivatives(prob)
sd_init_jacobian(prob)
sd_init_jacobian_coo(prob)
sd_init_hessian_coo(prob)
sd_objective_forward(prob, u)
sd_constraint_forward(prob, u)
sd_gradient(prob)
sd_jacobian_sparsity(prob)
sd_jacobian_values(prob)
sd_hessian_sparsity(prob)
sd_hessian_values(prob, obj_w, w)
sd_jacobian(prob)
sd_get_jacobian(prob)
sd_init_hessian(prob)
sd_hessian(prob, obj_w, w)
sd_get_hessian(prob)

Arguments

prob

a problem handle from sd_problem.

u

a numeric vector: the primal point at which to evaluate, laid out in the engine's column-major flat ordering (the same ordering used by the var_id offsets passed to sd_variable).

obj_w

a scalar weight \(\sigma\) multiplying the objective Hessian.

w

a numeric vector of constraint multipliers (length equal to the total constraint size) weighting the constraint Hessians.

Value

sd_init_derivatives, sd_init_jacobian, sd_init_jacobian_coo, sd_init_hessian, sd_init_hessian_coo

called for their side effect; return NULL invisibly.

sd_jacobian, sd_get_jacobian, sd_hessian, sd_get_hessian

a list with the CSR arrays of the matrix: data (double), indices (0-based column indices) and indptr (row pointers), plus shape = c(nrow, ncol). sd_jacobian evaluates the constraint Jacobian (after sd_init_jacobian and a forward pass) and sd_hessian the full Lagrangian Hessian \(\sigma\nabla^2 f + \sum_i w_i \nabla^2 g_i\) (after sd_init_hessian); the sd_get_* forms return the matrix as last evaluated, without re-evaluating it.

sd_objective_forward

the scalar objective value at u.

sd_constraint_forward

the constraint vector at u.

sd_gradient

the objective gradient, length n_vars.

sd_jacobian_sparsity, sd_hessian_sparsity

a list with integer rows/cols (0-based COO indices) and nrow/ncol.

sd_jacobian_values

the constraint-Jacobian nonzeros, matching the Jacobian sparsity order.

sd_hessian_values

the nonzeros of \(\sigma\nabla^2 f + \sum_i w_i \nabla^2 g_i\), lower triangle, matching the Hessian sparsity order.

Details

Evaluation is ordered: a forward pass first (sd_objective_forward / sd_constraint_forward) populates the node values at u, after which sd_gradient, sd_jacobian_values and sd_hessian_values read them. Sparsity patterns are structural — fixed once the corresponding sd_init_* routine has run — so they are queried once and reused, while the values are recomputed at each new point. Row and column indices are 0-based (the engine convention; a higher-level modeling layer such as CVXR translates them to 1-based as needed).

See also

sd_problem