MATLAB: How to index lmi constraints

Question

Dear Sir/Madam I have a nx1 index set Code for sdpvar object K and want to constrain elements of K to be pairwise distinct. I am using yalmip with the following constaint. F =[F, implies(a1, K(i)-K(ii)<= -.5*rand(1)), implies(a2, K(i)-K(ii) >= .5*rand(1)), a1+a2==1]; where a1 and a2 are binary. I want to include this constraint inside nested loops for all pairs (i,ii) with ii>i both belonging to Code. What is the easiest way to do this preferably in a vectorized manner?

Answer 1

Something like this would be a complete vectorization

n = 3;
[i,ii] = find(triu(ones(n),1));
index = sub2ind([n n],i,ii)
a1 = binvar(length(i),1);
a2 = binvar(length(i),1);
K = sdpvar(n);
F = [implies(a1, K(index) <= -0.1), implies(a2, K(index) >= 0.1), a1 + a2 == 1]