fmincon function with two non-linear constraints

hi all, I am trying to use the fmincon function to optimise a function with two non-linear constraints. The cost function is

for n = 1:N
    e = e + (norm(x(:, n) - o - dot(x(:, n), a)*a) - r)^2
end

where x is 3 by N matrix, o and a are three-dimension vectors and r is a scalar.

There are two constraints used

dot(a, o) == 0
norm(a) == 1

Can I use fmincon with two non-linear equal constraints? I saw the constraint function should contain a equal and non-equal constraints. How can I write the constraint function for my case?

Thank you

Answer 1

[Matt J]

Only one of your constraints is nonlinear. You could write it like so,

    function [c,ceq]=nonlcon(a)

      c=[]; 
      ceq=norm(a)^2-1;

    end

Your objective function is non-differentiable, however. You'll probably have to use instead

    e = e + (norm(x(:, n) - o - dot(x(:, n), a)*a)^2 - r^2)^2

[Ben]

Hi Matt, thank you for your reply. But in the nonlocn function, only the second constraint was used. How about the first one (dot(a, o) == 0)? Thank you

[Matt J]

As I mentioned, you only have 1 nonlinear constraint. The other one is linear. Use the Aeq and beq inputs to specify that one.

[Ben]

Thank you. I will have a try