Function "NONCVXUN"

[mahaa2]

Hi,

Using the packages OptimizationProblems and ADNLPProblems,
it seems that the function above does not have unique minimum as it is written in its description.

Actually seems to have many.

Please check.

[tmigot]

Hi @mahaa2 ! Is this a question about OptimizationProblems.jl more than CUTEst.jl?
It is possible that the comment is not correct, could you elaborate on why do you think it is the case?

[mahaa2]

Hi @tmigot,

I believe the function with identifier "NONCVXUN" implemented in ADNLPProblems
which I also believe it is the same as in the package CUTEst.jl,
has no unique minimum as is it written in its description, follows -

https://bitbucket.org/optrove/sif/raw/HEAD/NONCVXUN.SIF

[tmigot]

Is it a simple feeling or is there any evidence that there is more than one minimum?

[mahaa2]

Set the model. Given it random initial values. For each of them optimize the function, and set very small criteria. (discrepancy between consecutive function values and gradients)

It seems to end up in different points optimal points.

[tmigot]

Ok, interesting. Though, this needs to be verified analytically too, because the solvers stop at stationary points that could be minima or saddle points.