how to write the nonlinear constraints in fmincon

Hi everyone,

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

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

So the objective function I write is

 function Fexternal=myfun(x)

x1=x(1);

x2=x(2);

x3=x(3);

Fexternal=-(x1^2+x2^2+x3^2).

x is the 3*1 vector design variable in this problem.

However, there are also some other nonlinear constraints for this problem, i.e.

F1<=120;

F2<=100;

F3<=130;

F4<=140;

F5<=150;

F6<=20.

and F1~F6 are all the functions of the three variables x1~x3,i.e.

F1= F1(x(1),x(2),x(3));

F2= F2(x(1),x(2),x(3));

F3= F3(x(1),x(2),x(3));

F4= F4(x(1),x(2),x(3));

F5= F5(x(1),x(2),x(3));

F6= F6(x(1),x(2),x(3));

They are all long expressions and not simple to write all them explicitly.

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

THX very much for your help!

Answer 1

[George Papazafeiropoulos]

Define the constraint function as follows:

function [C,Ceq]=confun(x)
F1=...
F2=...
F3=...
F4=...
F5=...
F6=...
C=[F1-120;F2-100;F3-130;F4-140;F5-150;F6-20];
Ceq=[];

and use the command:

X = fmincon('Fexternal',x0,[],[],[],[],[],[],'confun')

Answer 2

[Stanley Cheng]

Hi George,

First thx very much for your input!

However, in the functions of F1~F6, there are other variables g, which are also used in the main m.file.

Besides, the x1~x3 are not explicitly expressed in F1~F6:

f1=f1(x1~x3,g);

f2=f2(x1~x3,g);

f3=f3(x1~x3,g);

and

F1=F1(f1,f2,f3);

F2=F2(f1,f2,f3);

F3=F3(f1,f2,f3);

F4=F4(f1,f2,f3);

F5=F5(f1,f2,f3);

F6=F6(f1,f2,f3);

These are the hard points...