Share system of equations solution between g(x) and dg(x)dx functions (i.e. constraint and its jacobian) in IPOPT

Specific Domains Optimization (Mathematical)
, ,
1

Hi,
I planning to use IPOPT in an optimization project.

I would like to know if there is a way to share the solution of a system of equations (like Ax=b) between different functions called by IPOPT, say the constraint and its jacobian functions. Because otherwise Ax=b needs to be solved twice, once per function call, g and dgdx.

Thanks!

2

It seems difficult even at C API level because we don’t know the order Ipopt calls eval_g and eval_jac_g (I am not sure if Ipopt guarantees the order to call user-provided functions). Otherwise we can solve Ax=b in eval_g and use the result directly in eval_jac_g.
Maybe a silly solution is to create an extra array to memorize recent values of x and corresponding solution of expensive Ax=b (for example, latest 5 values of x), then check the distance between current x and previously encountered x. If the distance is small enough, the memorized equation solution can be used directly.

1 Like
3

Thanks, you are right. We do not know the order of function calls and hence who comes first…
The solution you propose makes sense, thanks. But I think it requires to have global variables(or arrays) and to check whether their value has changed since the last function call before solving again the system within a certain function. Right?

4

Yep. I am afraid that global state is inevitable because we need more information beyond arguments of eval_g and eval_jac_g : x and the output array.

1 Like
5

It is what it is! Thanks again for your attention!

6

https://jump.dev/JuMP.jl/dev/examples/nlp_tricks/#User-defined-functions-with-vector-outputs

1 Like
7

Here the working link: https://jump.dev/JuMP.jl/dev/examples/Nonlinear%20programs/nlp_tricks/

1 Like