# Writing nonlinear constraint in fmincon

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george pepper on 23 Oct 2020
Commented: george pepper on 27 Oct 2020
Hello,
I minimize a function with 4 parameters on fmincon. The vector of parameters is b=[a1 a2 b1 b2 ]. How can I add a nonlinear constraint such that 5/b1<b2?
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george pepper on 27 Oct 2020
Thanks a lot! This is great.

Walter Roberson on 24 Oct 2020
5/b1 < b2 implies 5 < b2*b1 implies 0 < b2*b1 - 5 implies b2*b1 - 5 < 0 implies b2*b1 - 5 + delta = 0 for some positive delta.
delta = eps(realmin);
b(3)*b(4) - 5 + delta %<= 0 implied
However I would suggest you think more about your boundary constraint. Is 5/b1 == b2 an actual problem for your situation? If it is then you run serious risks that due to round-off issues, that whatever calculation fails with 5/b1 == b2, will not round in a "fortunate" way.
I personally would probably not use eps(realmin) for the delta: I would be more likely to use 5*(1-eps) instead of 5+delta
george pepper on 27 Oct 2020
Thank you very much!