[SCIP] Division by variable which is running to zero

[Pelda, Johannes]

Dear SCIP-Team,

Thank you very much for sharing this amazing solver!

I have the following question:

f(x, y, z) = (x - a)  * b * y * (1 - exp(-c / (b * y))) + z
f(x, y, z) = 0

With y running to zero the division is not defined and SCIP does not find a solution (infeasible, solution for z is 1e-20).
Adding a tiny number to y makes SKIP finding a solution.

f(x, y, z) = (x - a)  * b * y * (1 - exp(-c / (b * (y + 1e-20)))) + z
f(x, y, z) = 0

The question is how to determine the thiny number beforehand. The tiny number seems to depend on the size of the problem (for many x, y, z it happens that no solution can be found).
However, is there a better technique to solve the undefined problem for -c / (b * y) for y == 0, or to even linearize the function?

I am looking forward to your response.

Kind regards,
Johannes Pelda



Johannes Pelda
Nachhaltige Energie- und Umwelttechnik (NEUTec)

HAWK
Hochschule für angewandte Wissenschaft und Kunst Hildesheim/Holzminden/Göttingen
Fakultät Ressourcenmanagement | Rudolf-Diesel-Straße 12 | 37075 Göttingen
E-Mail: johannes.pelda at hawk.de<mailto:johannes.pelda at hawk.de> | Telefon: +49 551 5032 185
www.hawk.de<http://www.hawk.de/>


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