API

As stated in the Home page, we consider the nonlinear optimization problem in the following format:

\[\begin{aligned} \min \quad & f(x) \\ & c_L \leq c(x) \leq c_U \\ & \ell \leq x \leq u. \end{aligned}\]

To develop an optimization algorithm, we are usually worried not only with $f(x)$ and $c(x)$, but also with their derivatives. Namely,

$\nabla f(x)$, the gradient of $f$ at the point $x$;
$\nabla^2 f(x)$, the Hessian of $f$ at the point $x$;
$J(x) = \nabla c(x)^T$, the Jacobian of $c$ at the point $x$;
$\nabla^2 f(x) + \sum_{i=1}^m \lambda_i \nabla^2 c_i(x)$, the Hessian of the Lagrangian function at the point $(x,\lambda)$.

There are many ways to access some of these values, so here is a little reference guide.

Reference guide

The following naming should be easy enough to follow. If not, click on the link and go to the description.

! means inplace;
_coord means coordinate format;
prod means matrix-vector product;
_op means operator (as in LinearOperators.jl);
_lin and _nln respectively refer to linear and nonlinear constraints.

Feel free to open an issue to suggest other methods that should apply to all NLPModels instances.

Function	NLPModels function
$f(x)$	`obj`, `objgrad`, `objgrad!`, `objcons`, `objcons!`
$\nabla f(x)$	`grad`, `grad!`, `objgrad`, `objgrad!`
$\nabla^2 f(x)$	`hess`, `hess_op`, `hess_op!`, `hess_coord`, `hess_coord`, `hess_structure`, `hess_structure!`, `hprod`, `hprod!`
$c(x)$	`cons_lin`, `cons_lin!`, `cons_nln`, `cons_nln!`, `cons`, `cons!`, `objcons`, `objcons!`
$J(x)$	`jac_lin`, `jac_nln`, `jac`, `jac_lin_op`, `jac_lin_op!`, `jac_nln_op`, `jac_nln_op!`,`jac_op`, `jac_op!`, `jac_lin_coord`, `jac_lin_coord!`, `jac_nln_coord`, `jac_nln_coord!`, `jac_coord`, `jac_coord!`, `jac_lin_structure`, `jac_lin_structure!`, `jac_nln_structure`, `jac_nln_structure!`, `jac_structure`, `jprod_lin`, `jprod_lin!`, `jprod_nln`, `jprod_nln!`, `jprod`, `jprod!`, `jtprod_lin`, `jtprod_lin!`, `jtprod_nln`, `jtprod_nln!`, `jtprod`, `jtprod!`
$\nabla^2 L(x,y)$	`hess`, `hess_op`, `hess_coord`, `hess_coord!`, `hess_structure`, `hess_structure!`, `hprod`, `hprod!`, `jth_hprod`, `jth_hprod!`, `jth_hess`, `jth_hess_coord`, `jth_hess_coord!`, `ghjvprod`, `ghjvprod!`

API for NLSModels

For the Nonlinear Least Squares models, $f(x) = \tfrac{1}{2} \Vert F(x)\Vert^2$, and these models have additional function to access the residual value and its derivatives. Namely,

$J_F(x) = \nabla F(x)^T$
$\nabla^2 F_i(x)$

Function	function
$F(x)$	`residual`, `residual!`
$J_F(x)$	`jac_residual`, `jac_coord_residual`, `jac_coord_residual!`, `jac_structure_residual`, `jprod_residual`, `jprod_residual!`, `jtprod_residual`, `jtprod_residual!`, `jac_op_residual`, `jac_op_residual!`
$\nabla^2 F_i(x)$	`hess_residual`, `hess_coord_residual`, `hess_coord_residual!`, `hess_structure_residual`, `hess_structure_residual!`, `jth_hess_residual`, `hprod_residual`, `hprod_residual!`, `hess_op_residual`, `hess_op_residual!`

AbstractNLPModel functions

NLPModels.obj — Function

f = obj(nlp, x)

Evaluate $f(x)$, the objective function of nlp at x.

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NLPModels.grad — Function

g = grad(nlp, x)

Evaluate $∇f(x)$, the gradient of the objective function at x.

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NLPModels.grad! — Function

g = grad!(nlp, x, g)

Evaluate $∇f(x)$, the gradient of the objective function at x in place.

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NLPModels.objgrad — Function

f, g = objgrad(nlp, x)

Evaluate $f(x)$ and $∇f(x)$ at x.

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NLPModels.objgrad! — Function

f, g = objgrad!(nlp, x, g)

Evaluate $f(x)$ and $∇f(x)$ at x. g is overwritten with the value of $∇f(x)$.

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f, g = objgrad!(nls, x, g)
f, g = objgrad!(nls, x, g, Fx)

Evaluate f(x) and ∇f(x) of nls::AbstractNLSModel at x. Fx is overwritten with the value of the residual F(x).

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NLPModels.cons — Function

c = cons(nlp, x)

Evaluate $c(x)$, the constraints at x.

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NLPModels.cons! — Function

c = cons!(nlp, x, c)

Evaluate $c(x)$, the constraints at x in place.

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NLPModels.cons_lin — Function

c = cons_lin(nlp, x)

Evaluate the linear constraints at x.

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NLPModels.cons_lin! — Function

c = cons_lin!(nlp, x, c)

Evaluate the linear constraints at x in place.

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NLPModels.cons_nln — Function

c = cons_nln(nlp, x)

Evaluate the nonlinear constraints at x.

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NLPModels.cons_nln! — Function

c = cons_nln!(nlp, x, c)

Evaluate the nonlinear constraints at x in place.

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NLPModels.objcons — Function

f, c = objcons(nlp, x)

Evaluate $f(x)$ and $c(x)$ at x.

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NLPModels.objcons! — Function

f = objcons!(nlp, x, c)

Evaluate $f(x)$ and $c(x)$ at x. c is overwritten with the value of $c(x)$.

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NLPModels.jac_coord — Function

vals = jac_coord(nlp, x)

Evaluate $J(x)$, the constraints Jacobian at x in sparse coordinate format.

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NLPModels.jac_coord! — Function

vals = jac_coord!(nlp, x, vals)

Evaluate $J(x)$, the constraints Jacobian at x in sparse coordinate format, rewriting vals.

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NLPModels.jac_lin_coord — Function

vals = jac_lin_coord(nlp, x)

Evaluate $J(x)$, the linear constraints Jacobian at x in sparse coordinate format.

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NLPModels.jac_lin_coord! — Function

vals = jac_lin_coord!(nlp, x, vals)

Evaluate $J(x)$, the linear constraints Jacobian at x in sparse coordinate format, overwriting vals.

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NLPModels.jac_nln_coord — Function

vals = jac_nln_coord(nlp, x)

Evaluate $J(x)$, the nonlinear constraints Jacobian at x in sparse coordinate format.

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NLPModels.jac_nln_coord! — Function

vals = jac_nln_coord!(nlp, x, vals)

Evaluate $J(x)$, the nonlinear constraints Jacobian at x in sparse coordinate format, overwriting vals.

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NLPModels.jac_structure — Function

(rows,cols) = jac_structure(nlp)

Return the structure of the constraints Jacobian in sparse coordinate format.

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NLPModels.jac_structure! — Function

jac_structure!(nlp, rows, cols)

Return the structure of the constraints Jacobian in sparse coordinate format in place.

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NLPModels.jac_lin_structure — Function

(rows,cols) = jac_lin_structure(nlp)

Return the structure of the linear constraints Jacobian in sparse coordinate format.

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NLPModels.jac_lin_structure! — Function

jac_lin_structure!(nlp, rows, cols)

Return the structure of the linear constraints Jacobian in sparse coordinate format in place.

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NLPModels.jac_nln_structure — Function

(rows,cols) = jac_nln_structure(nlp)

Return the structure of the nonlinear constraints Jacobian in sparse coordinate format.

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NLPModels.jac_nln_structure! — Function

jac_nln_structure!(nlp, rows, cols)

Return the structure of the nonlinear constraints Jacobian in sparse coordinate format in place.

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NLPModels.jac — Function

Jx = jac(nlp, x)

Evaluate $J(x)$, the constraints Jacobian at x as a sparse matrix.

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NLPModels.jac_lin — Function

Jx = jac_lin(nlp, x)

Evaluate $J(x)$, the linear constraints Jacobian at x as a sparse matrix.

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NLPModels.jac_nln — Function

Jx = jac_nln(nlp, x)

Evaluate $J(x)$, the nonlinear constraints Jacobian at x as a sparse matrix.

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NLPModels.jac_op — Function

J = jac_op(nlp, x)

Return the Jacobian at x as a linear operator. The resulting object may be used as if it were a matrix, e.g., J * v or J' * v.

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NLPModels.jac_op! — Function

J = jac_op!(nlp, x, Jv, Jtv)

Return the Jacobian at x as a linear operator. The resulting object may be used as if it were a matrix, e.g., J * v or J' * v. The values Jv and Jtv are used as preallocated storage for the operations.

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J = jac_op!(nlp, rows, cols, vals, Jv, Jtv)

Return the Jacobian given by (rows, cols, vals) as a linear operator. The resulting object may be used as if it were a matrix, e.g., J * v or J' * v. The values Jv and Jtv are used as preallocated storage for the operations.

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NLPModels.jac_lin_op — Function

J = jac_lin_op(nlp, x)

Return the linear Jacobian at x as a linear operator. The resulting object may be used as if it were a matrix, e.g., J * v or J' * v.

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NLPModels.jac_lin_op! — Function

J = jac_lin_op!(nlp, x, Jv, Jtv)

Return the linear Jacobian at x as a linear operator. The resulting object may be used as if it were a matrix, e.g., J * v or J' * v. The values Jv and Jtv are used as preallocated storage for the operations.

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J = jac_lin_op!(nlp, rows, cols, vals, Jv, Jtv)

Return the linear Jacobian given by (rows, cols, vals) as a linear operator. The resulting object may be used as if it were a matrix, e.g., J * v or J' * v. The values Jv and Jtv are used as preallocated storage for the operations.

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NLPModels.jac_nln_op — Function

J = jac_nln_op(nlp, x)

Return the nonlinear Jacobian at x as a linear operator. The resulting object may be used as if it were a matrix, e.g., J * v or J' * v.

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NLPModels.jac_nln_op! — Function

J = jac_nln_op!(nlp, x, Jv, Jtv)

Return the nonlinear Jacobian at x as a linear operator. The resulting object may be used as if it were a matrix, e.g., J * v or J' * v. The values Jv and Jtv are used as preallocated storage for the operations.

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J = jac_nln_op!(nlp, rows, cols, vals, Jv, Jtv)

Return the nonlinear Jacobian given by (rows, cols, vals) as a linear operator. The resulting object may be used as if it were a matrix, e.g., J * v or J' * v. The values Jv and Jtv are used as preallocated storage for the operations.

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NLPModels.jprod — Function

Jv = jprod(nlp, x, v)

Evaluate $J(x)v$, the Jacobian-vector product at x.

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NLPModels.jprod! — Function

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

Evaluate $J(x)v$, the Jacobian-vector product at x in place.

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

Evaluate $J(x)v$, the Jacobian-vector product, where the Jacobian is given by (rows, cols, vals) in triplet format.

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NLPModels.jprod_lin — Function

Jv = jprod_lin(nlp, x, v)

Evaluate $J(x)v$, the linear Jacobian-vector product at x.

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NLPModels.jprod_lin! — Function

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

Evaluate $J(x)v$, the linear Jacobian-vector product at x in place.

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NLPModels.jprod_nln — Function

Jv = jprod_nln(nlp, x, v)

Evaluate $J(x)v$, the nonlinear Jacobian-vector product at x.

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NLPModels.jprod_nln! — Function

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

Evaluate $J(x)v$, the nonlinear Jacobian-vector product at x in place.

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NLPModels.jtprod — Function

Jtv = jtprod(nlp, x, v, Jtv)

Evaluate $J(x)^Tv$, the transposed-Jacobian-vector product at x.

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NLPModels.jtprod! — Function

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

Evaluate $J(x)^Tv$, the transposed-Jacobian-vector product at x in place. If the problem has linear and nonlinear constraints, this function allocates.

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

Evaluate $J(x)^Tv$, the transposed-Jacobian-vector product, where the Jacobian is given by (rows, cols, vals) in triplet format.

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NLPModels.jtprod_lin — Function

Jtv = jtprod_lin(nlp, x, v, Jtv)

Evaluate $J(x)^Tv$, the linear transposed-Jacobian-vector product at x.

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NLPModels.jtprod_lin! — Function

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

Evaluate $J(x)^Tv$, the linear transposed-Jacobian-vector product at x in place.

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NLPModels.jtprod_nln — Function

Jtv = jtprod_nln(nlp, x, v, Jtv)

Evaluate $J(x)^Tv$, the nonlinear transposed-Jacobian-vector product at x.

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NLPModels.jtprod_nln! — Function

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

Evaluate $J(x)^Tv$, the nonlinear transposed-Jacobian-vector product at x in place.

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NLPModels.jth_hprod — Function

Hv = jth_hprod(nlp, x, v, j)

Evaluate the product of the Hessian of j-th constraint at x with the vector v.

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NLPModels.jth_hprod! — Function

Hv = jth_hprod!(nlp, x, v, j, Hv)

Evaluate the product of the Hessian of j-th constraint at x with the vector v in place.

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NLPModels.jth_hess — Function

Hx = jth_hess(nlp, x, j)

Evaluate the Hessian of j-th constraint at x as a sparse matrix with the same sparsity pattern as the Lagrangian Hessian. A Symmetric object wrapping the lower triangle is returned.

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NLPModels.jth_hess_coord — Function

vals = jth_hess_coord(nlp, x, j)

Evaluate the Hessian of j-th constraint at x in sparse coordinate format. Only the lower triangle is returned.

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NLPModels.jth_hess_coord! — Function

vals = jth_hess_coord!(nlp, x, j, vals)

Evaluate the Hessian of j-th constraint at x in sparse coordinate format, with vals of length nlp.meta.nnzh, in place. Only the lower triangle is returned.

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NLPModels.ghjvprod — Function

gHv = ghjvprod(nlp, x, g, v)

Return the vector whose i-th component is gᵀ ∇²cᵢ(x) v.

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NLPModels.ghjvprod! — Function

ghjvprod!(nlp, x, g, v, gHv)

Return the vector whose i-th component is gᵀ ∇²cᵢ(x) v in place.

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NLPModels.hess_coord — Function

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

Evaluate the objective Hessian at x in sparse coordinate format, with objective function scaled by obj_weight, i.e.,

\[σ ∇²f(x),\]

with σ = obj_weight . Only the lower triangle is returned.

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

Evaluate the Lagrangian Hessian at (x,y) in sparse coordinate format, with objective function scaled by obj_weight, i.e.,

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

with σ = obj_weight . Only the lower triangle is returned.

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NLPModels.hess_coord! — Function

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

Evaluate the Lagrangian Hessian at (x,y) in sparse coordinate format, with objective function scaled by obj_weight, i.e.,

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

with σ = obj_weight , overwriting vals. Only the lower triangle is returned.

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NLPModels.hess_structure — Function

(rows,cols) = hess_structure(nlp)

Return the structure of the Lagrangian Hessian in sparse coordinate format.

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NLPModels.hess_structure! — Function

hess_structure!(nlp, rows, cols)

Return the structure of the Lagrangian Hessian in sparse coordinate format in place.

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NLPModels.hess — Function

Hx = hess(nlp, x; obj_weight=1.0)

Evaluate the objective Hessian at x as a sparse matrix, with objective function scaled by obj_weight, i.e.,

\[σ ∇²f(x),\]

with σ = obj_weight . A Symmetric object wrapping the lower triangle is returned.

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Hx = hess(nlp, x, y; obj_weight=1.0)

Evaluate the Lagrangian Hessian at (x,y) as a sparse matrix, with objective function scaled by obj_weight, i.e.,

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

with σ = obj_weight . A Symmetric object wrapping the lower triangle is returned.

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NLPModels.hess_op — Function

H = hess_op(nlp, x; obj_weight=1.0)

Return the objective Hessian at x with objective function scaled by obj_weight as a linear operator. The resulting object may be used as if it were a matrix, e.g., H * v. The linear operator H represents

\[σ ∇²f(x),\]

with σ = obj_weight .

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H = hess_op(nlp, x, y; obj_weight=1.0)

Return the Lagrangian Hessian at (x,y) with objective function scaled by obj_weight as a linear operator. The resulting object may be used as if it were a matrix, e.g., H * v. The linear operator H represents

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

with σ = obj_weight .

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NLPModels.hess_op! — Function

H = hess_op!(nlp, x, Hv; obj_weight=1.0)

Return the objective Hessian at x with objective function scaled by obj_weight as a linear operator, and storing the result on Hv. The resulting object may be used as if it were a matrix, e.g., w = H * v. The vector Hv is used as preallocated storage for the operation. The linear operator H represents

\[σ ∇²f(x),\]

with σ = obj_weight .

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H = hess_op!(nlp, rows, cols, vals, Hv)

Return the Hessian given by (rows, cols, vals) as a linear operator, and storing the result on Hv. The resulting object may be used as if it were a matrix, e.g., w = H * v. The vector Hv is used as preallocated storage for the operation. The linear operator H represents

\[σ ∇²f(x),\]

with σ = obj_weight .

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H = hess_op!(nlp, x, y, Hv; obj_weight=1.0)

Return the Lagrangian Hessian at (x,y) with objective function scaled by obj_weight as a linear operator, and storing the result on Hv. The resulting object may be used as if it were a matrix, e.g., w = H * v. The vector Hv is used as preallocated storage for the operation. The linear operator H represents

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

with σ = obj_weight .

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NLPModels.hprod — Function

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

Evaluate the product of the objective Hessian at x with the vector v, with objective function scaled by obj_weight, where the objective Hessian is

\[σ ∇²f(x),\]

with σ = obj_weight .

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

Evaluate the product of the Lagrangian Hessian at (x,y) with the vector v, with objective function scaled by obj_weight, where the Lagrangian Hessian is

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

with σ = obj_weight .

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NLPModels.hprod! — Function

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

Evaluate the product of the Lagrangian Hessian at (x,y) with the vector v in place, with objective function scaled by obj_weight, where the Lagrangian Hessian is

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

with σ = obj_weight .

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LinearOperators.reset! — Function

reset!(counters)

Reset evaluation counters

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reset!(nlp)

Reset evaluation count in nlp

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NLPModels.reset_data! — Function

reset_data!(nlp)

Reset model data if appropriate. This method should be overloaded if a subtype of AbstractNLPModel contains data that should be reset, such as a quasi-Newton linear operator.

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AbstractNLSModel

NLPModels.NLSCounters — Type

NLSCounters

Struct for storing the number of functions evaluations for nonlinear least-squares models. NLSCounters also stores a Counters instance named counters.

NLSCounters()

Creates an empty NLSCounters struct.

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NLPModels.residual — Function

Fx = residual(nls, x)

Computes $F(x)$, the residual at x.

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NLPModels.residual! — Function

Fx = residual!(nls, x, Fx)

Computes $F(x)$, the residual at x.

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NLPModels.jac_residual — Function

Jx = jac_residual(nls, x)

Computes $J(x)$, the Jacobian of the residual at x.

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NLPModels.jac_coord_residual — Function

(rows,cols,vals) = jac_coord_residual(nls, x)

Computes the Jacobian of the residual at x in sparse coordinate format.

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NLPModels.jac_coord_residual! — Function

vals = jac_coord_residual!(nls, x, vals)

Computes the Jacobian of the residual at x in sparse coordinate format, rewriting vals. rows and cols are not rewritten.

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NLPModels.jac_structure_residual — Function

(rows,cols) = jac_structure_residual(nls)

Returns the structure of the constraint's Jacobian in sparse coordinate format.

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NLPModels.jac_structure_residual! — Function

(rows,cols) = jac_structure_residual!(nls, rows, cols)

Returns the structure of the constraint's Jacobian in sparse coordinate format in place.

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NLPModels.jprod_residual — Function

Jv = jprod_residual(nls, x, v)

Computes the product of the Jacobian of the residual at x and a vector, i.e., $J(x)v$.

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NLPModels.jprod_residual! — Function

Jv = jprod_residual!(nls, x, v, Jv)

Computes the product of the Jacobian of the residual at x and a vector, i.e., $J(x)v$, storing it in Jv.

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NLPModels.jtprod_residual — Function

Jtv = jtprod_residual(nls, x, v)

Computes the product of the transpose of the Jacobian of the residual at x and a vector, i.e., $J(x)^Tv$.

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NLPModels.jtprod_residual! — Function

Jtv = jtprod_residual!(nls, x, v, Jtv)

Computes the product of the transpose of the Jacobian of the residual at x and a vector, i.e., $J(x)^Tv$, storing it in Jtv.

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NLPModels.jac_op_residual — Function

Jx = jac_op_residual(nls, x)

Computes $J(x)$, the Jacobian of the residual at x, in linear operator form.

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NLPModels.jac_op_residual! — Function

Jx = jac_op_residual!(nls, x, Jv, Jtv)

Computes $J(x)$, the Jacobian of the residual at x, in linear operator form. The vectors Jv and Jtv are used as preallocated storage for the operations.

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Jx = jac_op_residual!(nls, rows, cols, vals, Jv, Jtv)

Computes $J(x)$, the Jacobian of the residual given by (rows, cols, vals), in linear operator form. The vectors Jv and Jtv are used as preallocated storage for the operations.

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NLPModels.hess_residual — Function

H = hess_residual(nls, x, v)

Computes the linear combination of the Hessians of the residuals at x with coefficients v. A Symmetric object wrapping the lower triangle is returned.

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NLPModels.hess_coord_residual — Function

vals = hess_coord_residual(nls, x, v)

Computes the linear combination of the Hessians of the residuals at x with coefficients v in sparse coordinate format.

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NLPModels.hess_coord_residual! — Function

vals = hess_coord_residual!(nls, x, v, vals)

Computes the linear combination of the Hessians of the residuals at x with coefficients v in sparse coordinate format, rewriting vals.

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NLPModels.hess_structure_residual — Function

(rows,cols) = hess_structure_residual(nls)

Returns the structure of the residual Hessian.

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NLPModels.hess_structure_residual! — Function

hess_structure_residual!(nls, rows, cols)

Returns the structure of the residual Hessian in place.

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NLPModels.jth_hess_residual — Function

Hj = jth_hess_residual(nls, x, j)

Computes the Hessian of the j-th residual at x.

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NLPModels.hprod_residual — Function

Hiv = hprod_residual(nls, x, i, v)

Computes the product of the Hessian of the i-th residual at x, times the vector v.

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NLPModels.hprod_residual! — Function

Hiv = hprod_residual!(nls, x, i, v, Hiv)

Computes the product of the Hessian of the i-th residual at x, times the vector v, and stores it in vector Hiv.

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NLPModels.hess_op_residual — Function

Hop = hess_op_residual(nls, x, i)

Computes the Hessian of the i-th residual at x, in linear operator form.

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NLPModels.hess_op_residual! — Function

Hop = hess_op_residual!(nls, x, i, Hiv)

Computes the Hessian of the i-th residual at x, in linear operator form. The vector Hiv is used as preallocated storage for the operation.

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