Building a symbolic Hessian function with ModelingToolkit.jl

General Usage
,
1

I seek to build a Hessian function for the Lagrangian using ModelingToolkit.jl. This Hessian function is supposed to take two (non-symbolic) functions as arguments. My question is, how would you “correctly” write (if possible) the following using the same idea as found in this post, or any available workaround? I couldn’t figure it out from the different docs.

ℒ = func1 + sum(λ .* func2)
ℋ = ModelingToolkit.hessian(ℒ, [vec1; λ])

hess,_ = ModelingToolkit.build_function(ℋ, [func1;func2;λ]; expression=Val{false})
hess(obj(inp1,inp2,inp3), constr(inp4, inp5, inp6), lbda)

where obj outputs the objective value, and constr outputs the constraints vector; λ is the Lagrange multiplier.

Thank you.

2

I don’t quite get the question. Looks like that would work fine, other than the build_function call needs to match the signature of what you want to be passing in, so

hess,_ = ModelingToolkit.build_function(ℋ, [func1;func2], λ; expression=Val{false})
1 Like
3

Thanks a lot. It truly works fine, I was passing the functions wrongly.

4

Hi @ChrisRackauckas , thanks again. How would one show the output as a matrix with numeric values?
Thanks.

5

once you create the function you just call it with the inputs. Are you actually using ModelingToolkit here or just Symbolics?

6

Yes, I’m using ModelingToolkit, and there are the symbolic Differential() terms in the output.

7

Wait so is this coming from an OptimizationSystem? What kind of system type?

8

(EDIT) Oops… Yes! Constrained OptimizationSystem.
The goal is to find an effective way to compute the Lagrangian Hessian (preferably symbolically store it as this is a large system).

A very similar description of the problem would be this post. I think the original poster settled with their approach (which works but may not be very efficient). For a system with a large number of parameters, I would prefer to store this Hessian symbolically in a function and provide the Lagrange multiplier (and other parameters) each time we call the function. This is what I attempt doing with ModelingToolkit.jl.

9

Okay yeah, when you do OptimizationProblem you can just pass the hes=true and it should generate it.

10

Thank you very much for your help Chris. I opted for a different tool. I saved this answer for later!