Nonlinear optimization in JuMP adding the analytic gradient expression

[mb96]

Hi, I am trying to solve a highly dimensional nonlinear optimization problem for which I have a function that maps a vector into a value and a its jacobian. I want to solve the problem providing the gradient but I can not find good resources that explain how to do so using the Optim package. Can anyone point to resources or provide a very simple example illustrating how to set up the problem?

Thanks in advance,
Miguel.

[odow]

Do you have only a single function to optimize? Are there other constraints? Integrality or bounds on the variables?

You can register a user-defined function in JuMP and provide the analytic gradient: Nonlinear Modeling · JuMP

[mb96]

Thanks!

I am trying to adapt the example in the documentation so that it takes in a vector instead its elements explicitly because in my problem I am solving a 15 dimensional problem. However, when I do this it assumes it is univariate function. I illustrate this below:

When I call the function I run into this error:

Any ideas on how to fix this?

Thanks a lot!

[Adedayo_Yusuff]

I think you should use splat f(x…).

There is an example on this in Nonlinear Modeling · JuMP.

f(x...) = (1 - x[1])^2 + 100 * (x[2] - x[1]^2)^2
function ∇f(g, x...)
    g[1] = 400 * x[1]^3 - 400 * x[1] * x[2] + 2 * x[1] - 2
    g[2] = 200 * (x[2] - x[1]^2)
    return
end
function ∇²f(H, x...)
    H[1, 1] = 1200 * x[1]^2 - 400 * x[2] + 2
    # H[1, 2] = -400 * x[1]  <-- Not needed. Fill the lower-triangular only.
    H[2, 1] = -400 * x[1]
    H[2, 2] = 200.0
    return
end

model = Model()
register(model, :rosenbrock, 2, f, ∇f, ∇²f)
@variable(model, x[1:2])
@NLobjective(model, Min, rosenbrock(x[1], x[2]))

[odow]

Ooops. I never replied to this.

@Adedayo_Yusuff is correct. You need to use the splatted syntax. You cannot pass a Vector as a single argument.