Implicit Constraints using fmincon

Hello,

I have the following otpimzation problem: The objective function is given by: f(x)=x_1+...+x_n+x_{n+1}+...x_{n+d} And the constraints are given by: -x_i-x_j- sqrt(x_{n+1}+...+x_{n+d}) for 1<=i<j<=n. My question is how i can define the matrix of constraints A using fmincon.

Can someone help me to do this? Thanks in advance.

Answer 1

[Torsten]

Use the nonlinear constraint c(x)<=0 instead of the linear constraint A*x<=b.

Best wishes

Torsten.

[Heborvi]

Thanks for ur answer. in fact i define my objective function as:

function f = objfun(r)
S=0;
n=3;
dimension=2;
for i=1:n
S=S+r(i);
end
for d=1:dimension
    S=S+r(n+d);
end
f=S;

and the constraints as:

function [c, ceq] = confun(r)
% Nonlinear inequality constraints
n=4;
c=zeros(n*(n-1)/2,1);
for i=1:n
    for j=i+1:n
    c(i)=r(i)+r(j)-1;
    end
end
% Nonlinear equality constraints
ceq = [];

and i got this error:

Attempted to access r(3); index out of bounds because numel(r)=2.

Do you have any idea?

Thanks again.

[Torsten]

You seem to have a solution vector with two elements, but you address r(3),r(4) and r(5) in the two routines from above - elements which do not exist.

Best wishes

Torsten.

[Heborvi]

Thank you so much