Reference

ParametricNLPModels

Parametric sensitivity interface for NLPModels: derivatives with respect to a parameter vector θ of length npar.

• $∂f/∂θ$: the objective gradient with respect to the parameters, npar, see grad_par
• $∂c/∂θ$: the constraints Jacobian with respect to the parameters, ncon × npar, see jac_par
• $∂²L/∂x∂θ$: the Lagrangian Hessian with respect to the variables and the parameters, nvar × npar, see hess_par
• $∂x^ℓ/∂θ$, $∂x^u/∂θ$, $∂c^ℓ/∂θ$, $∂c^u/∂θ$: the bounds with respect to the parameters, nvar × npar and ncon × npar, see lvar_jac_par

Sparse coordinate format follows NLPModels: (rows, cols, vals) with rows in the constraint or variable index and columns in the parameter index, repeated entries summed. Dimensions and availability come from ParametricNLPModelMeta through get_par_meta.

ParametricNLPModelMeta(; kwargs...)

Metadata for the derivatives with respect to the parameters.

• npar: number of parameters
• nnzo_par: number of nonzeros in $∂f/∂θ$
• nnzj_par: number of nonzeros in $∂c/∂θ$
• nnzh_par: number of nonzeros in $∂²L/∂x∂θ$
• nnzj_lvar_par, nnzj_uvar_par, nnzj_lcon_par, nnzj_ucon_par: number of nonzeros in $∂x^ℓ/∂θ$, $∂x^u/∂θ$, $∂c^ℓ/∂θ$, $∂c^u/∂θ$
• grad_par_available, jac_par_available, hess_par_available, jprod_par_available, jtprod_par_available, hprod_par_available, htprod_par_available: whether the function is implemented

get_grad_par_available(nlp)
get_grad_par_available(par_meta)

Return the value grad_par_available from par_meta or get_par_meta(nlp).

get_hess_par_available(nlp)
get_hess_par_available(par_meta)

Return the value hess_par_available from par_meta or get_par_meta(nlp).

get_hprod_par_available(nlp)
get_hprod_par_available(par_meta)

Return the value hprod_par_available from par_meta or get_par_meta(nlp).

get_htprod_par_available(nlp)
get_htprod_par_available(par_meta)

Return the value htprod_par_available from par_meta or get_par_meta(nlp).

get_jac_par_available(nlp)
get_jac_par_available(par_meta)

Return the value jac_par_available from par_meta or get_par_meta(nlp).

get_jprod_par_available(nlp)
get_jprod_par_available(par_meta)

Return the value jprod_par_available from par_meta or get_par_meta(nlp).

get_jtprod_par_available(nlp)
get_jtprod_par_available(par_meta)

Return the value jtprod_par_available from par_meta or get_par_meta(nlp).

get_nnzh_par(nlp)
get_nnzh_par(par_meta)

Return the value nnzh_par from par_meta or get_par_meta(nlp).

get_nnzj_lcon_par(nlp)
get_nnzj_lcon_par(par_meta)

Return the value nnzj_lcon_par from par_meta or get_par_meta(nlp).

get_nnzj_lvar_par(nlp)
get_nnzj_lvar_par(par_meta)

Return the value nnzj_lvar_par from par_meta or get_par_meta(nlp).

get_nnzj_par(nlp)
get_nnzj_par(par_meta)

Return the value nnzj_par from par_meta or get_par_meta(nlp).

get_nnzj_ucon_par(nlp)
get_nnzj_ucon_par(par_meta)

Return the value nnzj_ucon_par from par_meta or get_par_meta(nlp).

get_nnzj_uvar_par(nlp)
get_nnzj_uvar_par(par_meta)

Return the value nnzj_uvar_par from par_meta or get_par_meta(nlp).

get_nnzo_par(nlp)
get_nnzo_par(par_meta)

Return the value nnzo_par from par_meta or get_par_meta(nlp).

get_npar(nlp)
get_npar(par_meta)

Return the value npar from par_meta or get_par_meta(nlp).

θ = get_par(nlp)

Return the parameter vector.

get_par_meta(nlp)

Return the ParametricNLPModelMeta of nlp. Defaults to no parameters.

g = grad_par!(nlp, x, g)

Evaluate $∂f/∂θ(x)$, the gradient of the objective function with respect to the parameters at x in place.

g = grad_par(nlp, x)

Evaluate $∂f/∂θ(x)$, the gradient of the objective function with respect to the parameters at x.

Hxθ = hess_par(nlp, x, y; obj_weight=1.0)

Evaluate the Lagrangian Hessian with respect to the variables and the parameters $∂²L/∂x∂θ(x,y)$ at (x,y) as a sparse matrix, with objective function scaled by obj_weight, i.e.,

\[∂²L/∂x∂θ(x,y) = σ ∂²f/∂x∂θ(x) + \sum_i yᵢ ∂²cᵢ/∂x∂θ(x),\]

with σ = obj_weight.

Hxθ = hess_par(nlp, x; obj_weight=1.0)

Evaluate the objective Hessian with respect to the variables and the parameters $∂²f/∂x∂θ(x)$ at x as a sparse matrix, with objective function scaled by obj_weight, i.e.,

\[σ ∂²f/∂x∂θ(x),\]

with σ = obj_weight.

vals = hess_par_coord!(nlp, x, y, vals; obj_weight=1.0)

Evaluate the Lagrangian Hessian with respect to the variables and the parameters $∂²L/∂x∂θ(x,y)$ at (x,y) in sparse coordinate format, with objective function scaled by obj_weight, i.e.,

\[∂²L/∂x∂θ(x,y) = σ ∂²f/∂x∂θ(x) + \sum_i yᵢ ∂²cᵢ/∂x∂θ(x),\]

with σ = obj_weight, overwriting vals.

vals = hess_par_coord!(nlp, x, vals; obj_weight=1.0)

Evaluate the objective Hessian with respect to the variables and the parameters $∂²f/∂x∂θ(x)$ at x in sparse coordinate format, with objective function scaled by obj_weight, i.e.,

\[σ ∂²f/∂x∂θ(x),\]

with σ = obj_weight, overwriting vals.

vals = hess_par_coord(nlp, x, y; obj_weight=1.0)

Evaluate the Lagrangian Hessian with respect to the variables and the parameters $∂²L/∂x∂θ(x,y)$ at (x,y) in sparse coordinate format, with objective function scaled by obj_weight, i.e.,

\[∂²L/∂x∂θ(x,y) = σ ∂²f/∂x∂θ(x) + \sum_i yᵢ ∂²cᵢ/∂x∂θ(x),\]

with σ = obj_weight.

vals = hess_par_coord(nlp, x; obj_weight=1.0)

Evaluate the objective Hessian with respect to the variables and the parameters $∂²f/∂x∂θ(x)$ at x in sparse coordinate format, with objective function scaled by obj_weight, i.e.,

\[σ ∂²f/∂x∂θ(x),\]

with σ = obj_weight.

Hxθ = hess_par_dense!(nlp, x, y, Hxθ; obj_weight=1.0)

Evaluate the Lagrangian Hessian with respect to the variables and the parameters $∂²L/∂x∂θ(x,y)$ at (x,y) in dense format, overwriting Hxθ, with objective function scaled by obj_weight, i.e.,

\[∂²L/∂x∂θ(x,y) = σ ∂²f/∂x∂θ(x) + \sum_i yᵢ ∂²cᵢ/∂x∂θ(x),\]

with σ = obj_weight.

Hxθ = hess_par_dense!(nlp, x, Hxθ; obj_weight=1.0)

Evaluate the objective Hessian with respect to the variables and the parameters $∂²f/∂x∂θ(x)$ at x in dense format, overwriting Hxθ, with objective function scaled by obj_weight, i.e.,

\[σ ∂²f/∂x∂θ(x),\]

with σ = obj_weight.

hess_par_structure!(nlp, rows, cols)

Return the structure of the Lagrangian Hessian with respect to the variables and the parameters $∂²L/∂x∂θ$ in sparse coordinate format in place.

(rows,cols) = hess_par_structure(nlp)

Return the structure of the Lagrangian Hessian with respect to the variables and the parameters $∂²L/∂x∂θ$ in sparse coordinate format.

Hv = hprod_par!(nlp, rows, cols, vals, v, Hv)

Evaluate the product of the Lagrangian Hessian with respect to the variables and the parameters $∂²L/∂x∂θ$ given by (rows, cols, vals) in triplet format with the vector v in place.

Hv = hprod_par!(nlp, x, y, v, Hv; obj_weight=1.0)

Evaluate the product of the Lagrangian Hessian with respect to the variables and the parameters $∂²L/∂x∂θ(x,y)$ at (x,y) with the vector v in place, with objective function scaled by obj_weight, where the Lagrangian Hessian $∂²L/∂x∂θ(x,y)$ is

\[∂²L/∂x∂θ(x,y) = σ ∂²f/∂x∂θ(x) + \sum_i yᵢ ∂²cᵢ/∂x∂θ(x),\]

with σ = obj_weight. This function allocates.

Hv = hprod_par!(nlp, x, v, Hv; obj_weight=1.0)

Evaluate the product of the objective Hessian with respect to the variables and the parameters $∂²f/∂x∂θ(x)$ at x with the vector v in place, with objective function scaled by obj_weight, where the objective Hessian $∂²f/∂x∂θ(x)$ is

\[σ ∂²f/∂x∂θ(x),\]

with σ = obj_weight. This function allocates.

Hv = hprod_par(nlp, x, y, v; obj_weight=1.0)

Evaluate the product of the Lagrangian Hessian with respect to the variables and the parameters $∂²L/∂x∂θ(x,y)$ at (x,y) with the vector v, with objective function scaled by obj_weight, where the Lagrangian Hessian $∂²L/∂x∂θ(x,y)$ is

\[∂²L/∂x∂θ(x,y) = σ ∂²f/∂x∂θ(x) + \sum_i yᵢ ∂²cᵢ/∂x∂θ(x),\]

with σ = obj_weight.

Hv = hprod_par(nlp, x, v; obj_weight=1.0)

Evaluate the product of the objective Hessian with respect to the variables and the parameters $∂²f/∂x∂θ(x)$ at x with the vector v, with objective function scaled by obj_weight, where the objective Hessian $∂²f/∂x∂θ(x)$ is

\[σ ∂²f/∂x∂θ(x),\]

with σ = obj_weight.

Htv = htprod_par!(nlp, rows, cols, vals, v, Htv)

Evaluate the product of the transposed Lagrangian Hessian with respect to the variables and the parameters $∂²L/∂x∂θ^T$ given by (rows, cols, vals) in triplet format with the vector v in place.

Htv = htprod_par!(nlp, x, y, v, Htv; obj_weight=1.0)

Evaluate the product of the transposed Lagrangian Hessian with respect to the variables and the parameters $∂²L/∂x∂θ(x,y)^T$ at (x,y) with the vector v in place, with objective function scaled by obj_weight, where the Lagrangian Hessian $∂²L/∂x∂θ(x,y)$ is

\[∂²L/∂x∂θ(x,y) = σ ∂²f/∂x∂θ(x) + \sum_i yᵢ ∂²cᵢ/∂x∂θ(x),\]

with σ = obj_weight. This function allocates.

Htv = htprod_par!(nlp, x, v, Htv; obj_weight=1.0)

Evaluate the product of the transposed objective Hessian with respect to the variables and the parameters $∂²f/∂x∂θ(x)^T$ at x with the vector v in place, with objective function scaled by obj_weight, where the objective Hessian $∂²f/∂x∂θ(x)$ is

\[σ ∂²f/∂x∂θ(x),\]

with σ = obj_weight. This function allocates.

Htv = htprod_par(nlp, x, y, v; obj_weight=1.0)

Evaluate the product of the transposed Lagrangian Hessian with respect to the variables and the parameters $∂²L/∂x∂θ(x,y)^T$ at (x,y) with the vector v, with objective function scaled by obj_weight, where the Lagrangian Hessian $∂²L/∂x∂θ(x,y)$ is

\[∂²L/∂x∂θ(x,y) = σ ∂²f/∂x∂θ(x) + \sum_i yᵢ ∂²cᵢ/∂x∂θ(x),\]

with σ = obj_weight.

Htv = htprod_par(nlp, x, v; obj_weight=1.0)

Evaluate the product of the transposed objective Hessian with respect to the variables and the parameters $∂²f/∂x∂θ(x)^T$ at x with the vector v, with objective function scaled by obj_weight, where the objective Hessian $∂²f/∂x∂θ(x)$ is

\[σ ∂²f/∂x∂θ(x),\]

with σ = obj_weight.

Jθ = jac_par(nlp, x)

Evaluate $∂c/∂θ(x)$, the constraints Jacobian with respect to the parameters at x as a sparse matrix.

vals = jac_par_coord!(nlp, x, vals)

Evaluate $∂c/∂θ(x)$, the constraints Jacobian with respect to the parameters at x in sparse coordinate format, overwriting vals.

vals = jac_par_coord(nlp, x)

Evaluate $∂c/∂θ(x)$, the constraints Jacobian with respect to the parameters at x in sparse coordinate format.

Jθ = jac_par_dense!(nlp, x, Jθ)

Evaluate $∂c/∂θ(x)$, the constraints Jacobian with respect to the parameters at x in dense format, overwriting Jθ.

jac_par_structure!(nlp, rows, cols)

Return the structure of the constraints Jacobian with respect to the parameters $∂c/∂θ$ in sparse coordinate format in place.

(rows,cols) = jac_par_structure(nlp)

Return the structure of the constraints Jacobian with respect to the parameters $∂c/∂θ$ in sparse coordinate format.

Jv = jprod_par!(nlp, x, v, Jv)

Evaluate $∂c/∂θ(x)v$, the Jacobian-vector product with respect to the parameters at x in place. This function allocates.

Jv = jprod_par!(nlp, rows, cols, vals, v, Jv)

Evaluate $∂c/∂θ(x)v$, the Jacobian-vector product with respect to the parameters, where the Jacobian is given by (rows, cols, vals) in triplet format.

Jv = jprod_par(nlp, x, v)

Evaluate $∂c/∂θ(x)v$, the Jacobian-vector product with respect to the parameters at x.

Jtv = jtprod_par!(nlp, x, v, Jtv)

Evaluate $∂c/∂θ(x)^Tv$, the transposed-Jacobian-vector product with respect to the parameters at x in place. This function allocates.

Jtv = jtprod_par!(nlp, rows, cols, vals, v, Jtv)

Evaluate $∂c/∂θ(x)^Tv$, the transposed-Jacobian-vector product with respect to the parameters, where the Jacobian is given by (rows, cols, vals) in triplet format.

Jtv = jtprod_par(nlp, x, v)

Evaluate $∂c/∂θ(x)^Tv$, the transposed-Jacobian-vector product with respect to the parameters at x.

J = lcon_jac_par(nlp)

Evaluate $∂c^ℓ/∂θ$, the lcon bounds with respect to the parameters, as a sparse matrix.

vals = lcon_jac_par_coord!(nlp, vals)

Evaluate $∂c^ℓ/∂θ$, the lcon bounds with respect to the parameters, in sparse coordinate format, overwriting vals.

vals = lcon_jac_par_coord(nlp)

Evaluate $∂c^ℓ/∂θ$, the lcon bounds with respect to the parameters, in sparse coordinate format.

J = lcon_jac_par_dense!(nlp, J)

Evaluate $∂c^ℓ/∂θ$, the lcon bounds with respect to the parameters, in dense format, overwriting J.

lcon_jac_par_structure!(nlp, rows, cols)

Return the structure of $∂c^ℓ/∂θ$, the lcon bounds with respect to the parameters, in sparse coordinate format in place.

(rows,cols) = lcon_jac_par_structure(nlp)

Return the structure of $∂c^ℓ/∂θ$, the lcon bounds with respect to the parameters, in sparse coordinate format.

Jv = lcon_jprod_par!(nlp, v, Jv)

Evaluate $(∂c^ℓ/∂θ)v$, the Jacobian-vector product of the lcon bounds with respect to the parameters, in place. This function allocates.

Jv = lcon_jprod_par(nlp, v)

Evaluate $(∂c^ℓ/∂θ)v$, the Jacobian-vector product of the lcon bounds with respect to the parameters.

Jtv = lcon_jtprod_par!(nlp, v, Jtv)

Evaluate $(∂c^ℓ/∂θ)^Tv$, the transposed-Jacobian-vector product of the lcon bounds with respect to the parameters, in place. This function allocates.

Jtv = lcon_jtprod_par(nlp, v)

Evaluate $(∂c^ℓ/∂θ)^Tv$, the transposed-Jacobian-vector product of the lcon bounds with respect to the parameters.

J = lvar_jac_par(nlp)

Evaluate $∂x^ℓ/∂θ$, the lvar bounds with respect to the parameters, as a sparse matrix.

vals = lvar_jac_par_coord!(nlp, vals)

Evaluate $∂x^ℓ/∂θ$, the lvar bounds with respect to the parameters, in sparse coordinate format, overwriting vals.

vals = lvar_jac_par_coord(nlp)

Evaluate $∂x^ℓ/∂θ$, the lvar bounds with respect to the parameters, in sparse coordinate format.

J = lvar_jac_par_dense!(nlp, J)

Evaluate $∂x^ℓ/∂θ$, the lvar bounds with respect to the parameters, in dense format, overwriting J.

lvar_jac_par_structure!(nlp, rows, cols)

Return the structure of $∂x^ℓ/∂θ$, the lvar bounds with respect to the parameters, in sparse coordinate format in place.

(rows,cols) = lvar_jac_par_structure(nlp)

Return the structure of $∂x^ℓ/∂θ$, the lvar bounds with respect to the parameters, in sparse coordinate format.

Jv = lvar_jprod_par!(nlp, v, Jv)

Evaluate $(∂x^ℓ/∂θ)v$, the Jacobian-vector product of the lvar bounds with respect to the parameters, in place. This function allocates.

Jv = lvar_jprod_par(nlp, v)

Evaluate $(∂x^ℓ/∂θ)v$, the Jacobian-vector product of the lvar bounds with respect to the parameters.

Jtv = lvar_jtprod_par!(nlp, v, Jtv)

Evaluate $(∂x^ℓ/∂θ)^Tv$, the transposed-Jacobian-vector product of the lvar bounds with respect to the parameters, in place. This function allocates.

Jtv = lvar_jtprod_par(nlp, v)

Evaluate $(∂x^ℓ/∂θ)^Tv$, the transposed-Jacobian-vector product of the lvar bounds with respect to the parameters.

set_par!(nlp, θ)

Set the parameter vector to θ.

J = ucon_jac_par(nlp)

Evaluate $∂c^u/∂θ$, the ucon bounds with respect to the parameters, as a sparse matrix.

vals = ucon_jac_par_coord!(nlp, vals)

Evaluate $∂c^u/∂θ$, the ucon bounds with respect to the parameters, in sparse coordinate format, overwriting vals.

vals = ucon_jac_par_coord(nlp)

Evaluate $∂c^u/∂θ$, the ucon bounds with respect to the parameters, in sparse coordinate format.

J = ucon_jac_par_dense!(nlp, J)

Evaluate $∂c^u/∂θ$, the ucon bounds with respect to the parameters, in dense format, overwriting J.

ucon_jac_par_structure!(nlp, rows, cols)

Return the structure of $∂c^u/∂θ$, the ucon bounds with respect to the parameters, in sparse coordinate format in place.

(rows,cols) = ucon_jac_par_structure(nlp)

Return the structure of $∂c^u/∂θ$, the ucon bounds with respect to the parameters, in sparse coordinate format.

Jv = ucon_jprod_par!(nlp, v, Jv)

Evaluate $(∂c^u/∂θ)v$, the Jacobian-vector product of the ucon bounds with respect to the parameters, in place. This function allocates.

Jv = ucon_jprod_par(nlp, v)

Evaluate $(∂c^u/∂θ)v$, the Jacobian-vector product of the ucon bounds with respect to the parameters.

Jtv = ucon_jtprod_par!(nlp, v, Jtv)

Evaluate $(∂c^u/∂θ)^Tv$, the transposed-Jacobian-vector product of the ucon bounds with respect to the parameters, in place. This function allocates.

Jtv = ucon_jtprod_par(nlp, v)

Evaluate $(∂c^u/∂θ)^Tv$, the transposed-Jacobian-vector product of the ucon bounds with respect to the parameters.

J = uvar_jac_par(nlp)

Evaluate $∂x^u/∂θ$, the uvar bounds with respect to the parameters, as a sparse matrix.

vals = uvar_jac_par_coord!(nlp, vals)

Evaluate $∂x^u/∂θ$, the uvar bounds with respect to the parameters, in sparse coordinate format, overwriting vals.

vals = uvar_jac_par_coord(nlp)

Evaluate $∂x^u/∂θ$, the uvar bounds with respect to the parameters, in sparse coordinate format.

J = uvar_jac_par_dense!(nlp, J)

Evaluate $∂x^u/∂θ$, the uvar bounds with respect to the parameters, in dense format, overwriting J.

uvar_jac_par_structure!(nlp, rows, cols)

Return the structure of $∂x^u/∂θ$, the uvar bounds with respect to the parameters, in sparse coordinate format in place.

(rows,cols) = uvar_jac_par_structure(nlp)

Return the structure of $∂x^u/∂θ$, the uvar bounds with respect to the parameters, in sparse coordinate format.

Jv = uvar_jprod_par!(nlp, v, Jv)

Evaluate $(∂x^u/∂θ)v$, the Jacobian-vector product of the uvar bounds with respect to the parameters, in place. This function allocates.

Jv = uvar_jprod_par(nlp, v)

Evaluate $(∂x^u/∂θ)v$, the Jacobian-vector product of the uvar bounds with respect to the parameters.

Jtv = uvar_jtprod_par!(nlp, v, Jtv)

Evaluate $(∂x^u/∂θ)^Tv$, the transposed-Jacobian-vector product of the uvar bounds with respect to the parameters, in place. This function allocates.

Jtv = uvar_jtprod_par(nlp, v)

Evaluate $(∂x^u/∂θ)^Tv$, the transposed-Jacobian-vector product of the uvar bounds with respect to the parameters.