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how to write series of multiple non-linear constraints for optimization using fmincon in MATLAB?

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Maheen Fazal
Maheen Fazal on 13 Sep 2019
Commented: Maheen Fazal on 4 Oct 2019
Hi, I have serios of multiple non-linear constraints and i am stuck how to write them in MATLAB, please help me out how to write the overall sum for n values. I have attached the problem below.
constraints.png
e.g. if phi and tau are the optimal variables which are x(1) and x (2) and the value of beta = 5,
Rn is the sumrate of main code and Rn' is the sumrate threshold value (10*1000) ,
function [c,ceq]=constraints(x)
c(1)=?
c(2)=?
c(3)=?
c(4)=sumrate(x)-10*1000
ceq=[];
end
how to erite the other constraints?
thank you in advance
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Accepted Answer

xi
xi on 17 Sep 2019
Edited: Matt J on 17 Sep 2019
You have 2n parameters, named X1,X2...Xn(for phi) and Xn+1...X2n (for tau).
You need to write the constraints in the vectorized format of Ax-b<0, where A is a matrix, b is a vector. The #rows of A as well as the length of b is determined by how many contraints you have, and the #columns is 2n (number of parameters).
In your case, the first three sets of constraints are linear constraints (total of 1+1+2n=2n+2). Your A matrix should have 2n+2 rows:
A(1,:)= [ones(1,n),zeros(1,n)];
A(2,:)= [zeros(1,n),ones(1,n)];
A=[A;-eye(2*n)];
b=[(1-beta);beta;zeros(2*n,1)]
  10 Comments
Maheen Fazal
Maheen Fazal on 4 Oct 2019
Yes you are right, i have two parameters and for both parameters there are two separate equations.
constraintss.png
so for that i wrote linear inequality constraints like this as mentioned below, but still not getting the proper graph.
A=[ones(1,n),zeros(1,n);zeros(1,n),ones(1,n)]
b=[(1-B);B;];

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