Cmaes vs csminwel

What is the difference between cmaes and csminwel. why is csminwel preffered over CMAES. Please guide

csminwel is a Newton-type local optimizer. If you are close to the global mode, it will quickly converge to this this mode. But it can also converge to a local mode, i.e. fail to find the global one because it is local.
cmaes is a global optimizer. It will be slower but has a higher likelihood of finding the global mode instead of just a local one.

You mean cmaes is better option?? But in cmaes, it returns the upper or lower bound value of some parameters. Is that ok??

No, there is no general statement like that. They have different properties. For that reason, it is recommended to try both versions and use the one that has the best value of the objective function, i.e. returns the higher mode. Of course, the global model may indeed be a corner solution, but that’s the way it is.

when we talk about function best value, is it related to lower or higher value?

That depends on the function, i.e. if it’s an object that reported in the form of a loss function or not.