# non-linear optimization with complex constrains

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bo peng on 22 Dec 2020
Commented: bo peng on 13 May 2021
hi，my friends
i have a problem need your help
My problem as following:
min f(x)=s(1)+s(2)+s(3)
s.t.
s(1)=0.5x(1)^2+w
s(2)=-4x(2)+7
s(3)=-3x(3)^3+6x^2
x(1)+x(2)+x(3)=100
0<x(1)<x(2)<x(3)
where x(1)<20 then w=100,
else w =500
Do you know how to convert constrains to standard form ,g(x) >= 0
which function can solve the question above, thank you

Alan Weiss on 24 Dec 2020
I think that you need to solve two different problems, one assuming w =100, one assuming w = 500. Your objective is discontinuous at x(1) = 20, and Optimization Toolbox solvers cannot handle a discontinuous objective.
You could try a solver from Global Optimization Toolbox such as patternsearch.
Alan Weiss
MATLAB mathematical toolbox documentation
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bo peng on 13 May 2021
this is a good answer, i think you are right

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