Approach for handling non-linear equations

GAMS
1

Hi,

One of my constraints involves formulating this relationship between two variables x and y as shown in this picture:
image.png
Since this is a non-linear relationship, it becomes difficult to solve the problem. From my past experience, it is really difficult to get a solution for a non-linear problem (this turns my model to an MINLP). Can anyone suggest me what way should I approach to handle this issue?

Any reference to any opensource code implementation will be really helpful.

Regards,

2

Do you have a closed form algebra for the function? If so, just use it in an MINLP and try the MINLP solvers. If not, you can approximate. This function looks good for approximation by piecewise-linear functions. This has also the advantage to keep the model linear. There are a couple of examples for piecewise-linear functions in the GAMS Model Library, e.g. https://www.gams.com/39/gamslib_ml/libhtml/gamslib_trnspwl.html.

Good luck,
-Michael