fmincon optimization with nonlinear constraint

Dear All

I am using the fmincon in matlab to minimize the objective value as

F=-(x(1)^2+x(2)^2+x(3)^2-x(4)^2) .

i have the nonlinear constrain that

x(1)-x(3)=x(2)-x(4)

How can the nonlinear constraint functions to be written as a .m file?

THX very much for your help!

Answer 1

[Walter Roberson]

nonlcon = @(x) deal([], x(1)-x(3)-(x(2)-x(4)))

However, you should consider rewriting with one fewer variable.

x(1)-x(3)=x(2)-x(4)

implies x(4) = x(2) + x(3) - x(1) .

Substituting in F=-(x(1)^2+x(2)^2+x(3)^2-x(4)^2) we get

F = -(x(1).^2 + x(2).^2 + x(3).^2 - (x(2) + x(3) - x(1)).^2)

This simplifies to

F = 2*(x2*x3 - x1*x3 - x1*x2)

and since this is an optimization task, the linear scale is not relevant, so you can use

F = x2*x3 - x1*x3 - x1*x2;

No non-linear constraint would be needed.

[mohammed hussein]

Thank you very much for your answer