# Non-linear constraints with several input variables in fmincon

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javm6 on 16 Sep 2021
Edited: Matt J on 22 Sep 2021
Hello everyone,
I am trying to solve the following optimization problem with fmincon: To do this, I have made the following code:
fun = @(x) x'*L*x;
nonlcon = @(x) consfun(A,B,x);
x = fmincon(fun,x0,[],[],[],[],[],[],nonlcon);
Where ''consfun'' is the following function:
function [c,ceq] = consfun(A,B,x)
c = (norm(A*x,inf)/b)-D);
ceq = [];
end
However, the final solution, x, does not satisfy the non-linear constraint so I wonder if the code is correct in relation to the optimisation problem posed.
Can anyone help me?
Thank you very much for your time!
Alan Weiss on 20 Sep 2021
Did fmincon claim to give a feasible solution? If so, then in what way was the constraint violated? I mean, was consfun(A,B,x) > 0? If not, then you may need to search for a feasible solution. See Converged to an Infeasible Point.
Alan Weiss
MATLAB mathematical toolbox documentation

Matt J on 20 Sep 2021
Edited: Matt J on 20 Sep 2021
Your nonlinear constraints are not differentiable. That doesn't always spell disaster, but it breaks the assumptions of fmincon. Also, since your problem can be reformulated as a quadratic program, it would be better to use quadprog.
[m,n]=size(A);
e=ones(m,1);
Aineq=[A;-A];
bineq=[(B+b*D).*e ; -(B-b*D).*e];
Matt J on 22 Sep 2021
The reformulation is equivalent to the original, posted problem with the inf-norm constraints. The inf-norm constraint in the can be re-written as the linear system,
-b*D <= A*x-B <= b*D
or
A*x <= B+b*D
-A*x <= -(B-b*D)