API

f = obj(nlp, x)

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

g = grad(nlp, x)

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

g = grad!(nlp, x, g)

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

f, g = objgrad(nlp, x)

Evaluate $f(x)$ and $\nabla f(x)$ at x.

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

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

c = cons(nlp, x)

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

c = cons!(nlp, x, c)

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

f, c = objcons(nlp, x)

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

f = objcons!(nlp, x, c)

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

(rows,cols,vals) = jac_coord(nlp, x)

Evaluate $\nabla c(x)$, the constraint's Jacobian at x in sparse coordinate format.

Jx = jac(nlp, x)

Evaluate $\nabla c(x)$, the constraint's Jacobian at x as a sparse matrix.

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.

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.

Jv = jprod(nlp, x, v)

Evaluate $\nabla c(x)v$, the Jacobian-vector product at x.

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

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

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

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

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

Evaluate $\nabla c(x)^Tv$, the transposed-Jacobian-vector product at x in place.

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

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

\[ \nabla^2L(x,y) = \sigma * \nabla^2 f(x) + \sum_{i=1}^m y_i\nabla^2 c_i(x), \]

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

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

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

\[ \nabla^2L(x,y) = \sigma * \nabla^2 f(x) + \sum_{i=1}^m y_i\nabla^2 c_i(x), \]

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

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

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

\[ \nabla^2L(x,y) = \sigma * \nabla^2 f(x) + \sum_{i=1}^m y_i\nabla^2 c_i(x), \]

with σ = obj_weight.

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

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

\[ \nabla^2L(x,y) = \sigma * \nabla^2 f(x) + \sum_{i=1}^m y_i\nabla^2 c_i(x), \]

with σ = obj_weight.

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

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

\[ \nabla^2L(x,y) = \sigma * \nabla^2 f(x) + \sum_{i=1}^m y_i\nabla^2 c_i(x), \]

with σ = obj_weight.

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

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

\[ \nabla^2L(x,y) = \sigma * \nabla^2 f(x) + \sum_{i=1}^m y_i\nabla^2 c_i(x), \]

with σ = obj_weight.

mp = NLPtoMPB(nlp, solver)

Return a MathProgBase model corresponding to an AbstractNLPModel.

Arguments

• nlp::AbstractNLPModel

• solver::AbstractMathProgSolver a solver instance, e.g., IpoptSolver()

Currently, all models are treated as nonlinear models.

Return values

The function returns a MathProgBase model mpbmodel such that it should be possible to call

MathProgBase.optimize!(mpbmodel)

reset!(counters)

Reset evaluation counters

`reset!(nlp)

Reset evaluation count in nlp

Check the first derivatives of the objective at x against centered finite differences.

This function returns a dictionary indexed by components of the gradient for which the relative error exceeds rtol.

Check the first derivatives of the constraints at x against centered finite differences.

This function returns a dictionary indexed by (j, i) tuples such that the relative error in the i-th partial derivative of the j-th constraint exceeds rtol.

Check the second derivatives of the objective and each constraints at x against centered finite differences. This check does not rely on exactness of the first derivatives, only on objective and constraint values.

The sgn arguments refers to the formulation of the Lagrangian in the problem. It should have a positive value if the Lagrangian is formulated as

L(x,y) = f(x) + ∑ yⱼ cⱼ(x)

e.g., as in JuMPNLPModels, and a negative value if the Lagrangian is formulated as

L(x,y) = f(x) - ∑ yⱼ cⱼ(x)

e.g., as in AmplModels. Only the sign of sgn is important.

This function returns a dictionary indexed by functions. The 0-th function is the objective while the k-th function (for k > 0) is the k-th constraint. The values of the dictionary are dictionaries indexed by tuples (i, j) such that the relative error in the second derivative ∂²fₖ/∂xᵢ∂xⱼ exceeds rtol.

Check the second derivatives of the objective and each constraints at x against centered finite differences. This check assumes exactness of the first derivatives.

The sgn arguments refers to the formulation of the Lagrangian in the problem. It should have a positive value if the Lagrangian is formulated as

L(x,y) = f(x) + ∑ yⱼ cⱼ(x)

e.g., as in JuMPNLPModels, and a negative value if the Lagrangian is formulated as

L(x,y) = f(x) - ∑ yⱼ cⱼ(x)

e.g., as in AmplModels. Only the sign of sgn is important.

This function returns a dictionary indexed by functions. The 0-th function is the objective while the k-th function (for k > 0) is the k-th constraint. The values of the dictionary are dictionaries indexed by tuples (i, j) such that the relative error in the second derivative ∂²fₖ/∂xᵢ∂xⱼ exceeds rtol.