I have got an academic license of CVX and Gurobi for solving a 5 variable convex QCQP.
I found the following error:
Gurobi does not support semidefinite cones larger than 2x2.
Please someone suggest.
Thanking you/
The following problem is modelled:
clear all
close all
Q0=[163 -46 565/2 77/2 -3;-46 50 5984/2 -11 31/2;565/2 5984/2 55 11 2543/2; 77/2 -11 11 -8 -76/2;-3 31/2 2543/2 -76/2 5];
Q1=[2 2 0 0 0;2 2 0 0 0;0 0 0 0 0;0 0 0 0 0;0 0 0 0 0];
Q2=[0 0 0 0 0;0 0 0 0 0;0 0 0 0 0;0 0 0 0 0;0 0 0 0 0];
Q3=[1 0 0 0 0;0 0 0 0 0;0 0 0 0 0;0 0 0 0 0;0 0 0 0 0];
Q4=[0 0 0 0 0;0 1 0 0 0;0 0 0 0 0;0 0 0 0 0;0 0 0 0 0];
Q5=[0 0 0 0 0;0 0 0 0 0;0 0 1 0 0;0 0 0 0 0;0 0 0 0 0];
Q6=[0 0 0 0 0;0 0 0 0 0;0 0 0 0 0;0 0 0 1 0;0 0 0 0 0];
Q7=[0 0 0 0 0;0 0 0 0 0;0 0 0 0 0;0 0 0 0 0;0 0 0 0 1];
Q8=[-1 0 0 0 0;0 0 0 0 0;0 0 0 0 0;0 0 0 0 0;0 0 0 0 0];
Q9=[0 0 0 0 0;0 -1 0 0 0;0 0 0 0 0;0 0 0 0 0;0 0 0 0 0];
Q10=[0 0 0 0 0;0 0 0 0 0;0 0 -1 0 0;0 0 0 0 0;0 0 0 0 0];
Q11=[0 0 0 0 0;0 0 0 0 0;0 0 0 0 0;0 0 0 -1 0;0 0 0 0 0];
Q12=[0 0 0 0 0;0 0 0 0 0;0 0 0 0 0;0 0 0 0 0;0 0 0 0 -1];
Q=cat(13,Q1,Q2,Q3,Q4,Q5,Q6,Q7,Q8,Q9,Q10,Q11,Q12);
a=[8 1 -1 0 0 0 0 1 0 0 0 0;6 -2 0 -1 0 0 0 0 1 0 0 0;1 1 0 0 -1 0 0 0 0 1 0 0;-4 1 0 0 0 -1 0 0 0 0 1 0;0 1 0 0 0 0 -1 0 0 0 0 1];
b=[-9 -1 0 0 0 0 0 0 0 0 0 0];
m=12;n=5;
f_opt=-47;
cvx_solver gurobi
tic
cvx_begin sdp quiet
variable X(n,n) symmetric
variable x(n)
variable z(n,n) symmetric
variable y(n,n) symmetric
minimize(trace(Q0*X))
for i=1:m
trace(Q(:,:,i)*X)+a(:,i)'*x+b(i)<=0;
end
diag(X)==x;
%Adding RLT to SDP
for i=1:n
for j=i:n
if (i<=j)
x(i)+x(j)-X(i,j)<=1;
X(i,j)-x(i)<=0;
X(i,j)-x(j)<=0;
X(i,j)>=0;
end
end
end
% TI
%%
for i=1:n
for j=1:n
if(i~=j)
z(i,j)>=x(i);
z(i,j)>=x(j);
z(i,j)<=x(i)+1*(1-y(i,j));
z(i,j)<=x(j)+2.02*(y(i,j));
0.0<=y(i,j)<=1;
end
end
end
for i=1:n
for j=i:n
for k=j:n
if (i~=j && j<k && k~=i)
X(i,j)-X(i,k)-X(j,k)<=2*z(j,k)-2*x(k)-x(j);
end
end
end
end
% finally, the constraints
Y=[1, x'; x, X];
Y == semidefinite(n+1);
cvx_end
On the above problem I found the error message.