How to make a constraint for restricting two vectors on one line?

Nonconvex
1 
b=[1 1 1];c=[2 6];
A=[1 3 5;8 6 9];B=[6 2 8; 8 4 5];
cvx_begin
variables x(3) ;variables y(3);
minimize( b*abs(x)+b*abs(y));
subject to
norm(A*x+B*y-c',2)<=0.001;
cvx_end

i want to restrict vector x and vector y on one line, i mean that

x(1)/y(1)=x(2)/y(2)=x(3)/y(3),

and i make a constraint as follows:

norm(x,2)+norm(y,2)<=norm(x+y,2);

but this is Invalid constraint: {convex} <= {convex}
how can i express this constraint in CVX ?
this constraint is very important in my modle, thanks very much.

2

I do not think it is possible to express it as a convex problem. Please explain why you think it should be convex!