Asking for help with syntax for fmincon
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Hi all,
I am trying out the standard given examples in MATLAB for fmincon usage. I am referring to this particular example:
openExample('optim/NonlinearConstraintsExample')
fun = @(x) 100*(x(2)-x(1)^2)^2 + (1-x(1))^2;
lb = [0,0.2];
ub = [0.5,0.8];
function [c,ceq] = circlecon(x)
c = (x(1)-1/3)^2 + (x(2)-1/3)^2 - (1/3)^2;
ceq = [];
A = [];
b = [];
Aeq = [];
beq = [];
x0 = [1/4,1/4];
nonlcon = @circlecon;
x = fmincon(fun,x0,A,b,Aeq,beq,lb,ub,nonlcon)
I want to modify it to have multiple variables separately in separate vectors but still be able to solve the final problem. For example I make the following modification:
fun = @(x,y) 100*(x(2)-x(1)^2)^2 + (1-x(1))^2 + 100*(y(2)-y(1)^2)^2 + (1-y(1))^2;
lb = [0,0.2,0,0.2];
ub = [0.5,0.8,0.5,0.8];
function [c,ceq] = circlecon(x,y)
c = (x(1)-1/3)^2 + (x(2)-1/3)^2 - (1/3)^2 + (y(1)-1/3)^2 + (y(2)-1/3)^2 - (1/3)^2;
ceq = [];
A = [];
b = [];
Aeq = [];
beq = [];
x0 = [1/4,1/4];
y0 = [1/4,1/4];
nonlcon = @circlecon;
Notice that I have introduced a new 'y' variable. I can't figure out how to correctly call the fmincon function to solve the problem.
Kindly advise please.
Regards
0 Comments
Accepted Answer
Stephan
on 21 Oct 2020
Edited: Stephan
on 21 Oct 2020
The solvers in Matlab accept only one vector as variable. So change y(1) --> x(3) and y(2) --> x(4). Then edit the code this way and it will work:
fun = @(x) 100*(x(2)-x(1).^2).^2 + (1-x(1)).^2 + 100*(x(4)-x(3).^2).^2 + (1-x(3)).^2;
lb = [0,0.2,0,0.2];
ub = [0.5,0.8,0.5,0.8];
A = [];
b = [];
Aeq = [];
beq = [];
x0 = [1/4,1/4,1/4,1/4];
nonlcon = @circlecon;
x = fmincon(fun,x0,A,b,Aeq,beq,lb,ub,nonlcon)
function [c,ceq] = circlecon(x)
c = (x(1)-1/3).^2 + (x(2)-1/3).^2 - (1/3)^2 + (x(3)-1/3).^2 + (x(4)-1/3).^2 - (1/3)^2;
ceq = [];
end
3 Comments
Stephan
on 21 Oct 2020
Edited: Stephan
on 21 Oct 2020
Of course you can do something like this:
lb = [0,0.2,0,0.2];
ub = [0.5,0.8,0.5,0.8];
A = [];
b = [];
Aeq = [];
beq = [];
x0 = [1/4,1/4];
y0 = [1/4,1/4];
nonlcon = @circlecon;
x = fmincon(@fun,[x0 y0],A,b,Aeq,beq,lb,ub,nonlcon);
x_sol = x(1:2)
y_sol = x(3:4)
function myObj = fun(x)
y(1) = x(3);
y(2) = x(4);
myObj = 100*(x(2)-x(1).^2).^2 + (1-x(1)).^2 + 100*(y(2)-y(1).^2).^2 + (1-y(1)).^2;
end
function [c,ceq] = circlecon(x)
y(1) = x(3);
y(2) = x(4);
c = (x(1)-1/3).^2 + (x(2)-1/3).^2 - (1/3)^2 + (y(1)-1/3).^2 + (y(2)-1/3).^2 - (1/3)^2;
ceq = [];
end
But this does not change the fact, that the Matlab solvers like fmincon will only accept one vector with variables. On the other hand it might be easier to understand whats happening, by doing it this way. And a little bit you accepted this already, when you defined the lower and upper bounds ;-)
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