NLPModelsJuMP is a combination of NLPModels and JuMP, as the name implies. Sometimes it may be required to refer to the specific documentation, as we'll present here only the documention specific to NLPModelsJuMP.
MathOptNLPModel(model, hessian=true, name="Generic")
Construct a MathOptNLPModel from a JuMP model.
hessian should be set to false for multivariate user-defined functions registered without hessian.
MathOptNLPModel is a simple yet efficient model. It uses JuMP to define the problem, and can be accessed through the NLPModels API. An advantage of MathOptNLPModel over simpler models such as ADNLPModels is that they provide sparse derivates.
Let's define the famous Rosenbrock function
\[f(x) = (x_1 - 1)^2 + 100(x_2 - x_1^2)^2,\]
with starting point $x^0 = (-1.2,1.0)$.
using NLPModels, NLPModelsJuMP, JuMP
x0 = [-1.2; 1.0]
model = Model() # No solver is required
@@ -107,7 +107,7 @@
println("cx = $(cons(nlp, nlp.meta.x0))")
println("Jx = $(jac(nlp, nlp.meta.x0))")
cx = [-0.19999999999999996, -2.2]
-Jx = sparse([1, 2, 1, 2], [1, 1, 2, 2], [1.0, 1.0, 1.0, -1.2], 2, 2)
MathOptNLSModel(model, F, hessian=true, name="Generic")
Construct a MathOptNLSModel from a JuMP model and a container of JuMP GenericAffExpr (generated by @expression) and NonlinearExpression (generated by @NLexpression).
hessian should be set to false for multivariate user-defined functions registered without hessian.
MathOptNLSModel is a model for nonlinear least squares using JuMP, The objective function of NLS problems has the form $f(x) = \tfrac{1}{2}\|F(x)\|^2$, but specialized methods handle $F$ directly, instead of $f$. To use MathOptNLSModel, we define a JuMP model without the objective, and use NLexpressions to define the residual function $F$. For instance, the Rosenbrock function can be expressed in nonlinear least squares format by defining
\[F(x) = \begin{bmatrix} x_1 - 1\\ 10(x_2 - x_1^2) \end{bmatrix},\]
and noting that $f(x) = \|F(x)\|^2$ (the constant $\frac{1}{2}$ is ignored as it doesn't change the solution). We implement this function as
using NLPModels, NLPModelsJuMP, JuMP
+Jx = sparse([1, 2, 1, 2], [1, 1, 2, 2], [1.0, 1.0, 1.0, -1.2], 2, 2)
MathOptNLSModel(model, F, hessian=true, name="Generic")
Construct a MathOptNLSModel from a JuMP model and a container of JuMP GenericAffExpr (generated by @expression) and NonlinearExpression (generated by @NLexpression).
hessian should be set to false for multivariate user-defined functions registered without hessian.
MathOptNLSModel is a model for nonlinear least squares using JuMP, The objective function of NLS problems has the form $f(x) = \tfrac{1}{2}\|F(x)\|^2$, but specialized methods handle $F$ directly, instead of $f$. To use MathOptNLSModel, we define a JuMP model without the objective, and use NLexpressions to define the residual function $F$. For instance, the Rosenbrock function can be expressed in nonlinear least squares format by defining
\[F(x) = \begin{bmatrix} x_1 - 1\\ 10(x_2 - x_1^2) \end{bmatrix},\]
and noting that $f(x) = \|F(x)\|^2$ (the constant $\frac{1}{2}$ is ignored as it doesn't change the solution). We implement this function as
using NLPModels, NLPModelsJuMP, JuMP
model = Model()
x0 = [-1.2; 1.0]
@@ -121,4 +121,4 @@
-2.2
-4.3999999999999995
jac_residual(nls, nls.meta.x0)
2×2 SparseArrays.SparseMatrixCSC{Float64, Int64} with 3 stored entries:
1.0 ⋅
- 24.0 10.0
The package NLSProblems provides a collection of problems already defined as MathOptNLSModel.