SOC Constraint in cplexmiqcp

Hi,

I am trying to solve a problem which has a second-order cone constraint as follow

The code that I have is:

Qij= cell(1,J);
for j=1:J
Q=zeros(I*J+3*J+J*K+1+I+J+I*J);
Q((j-1)*I+1:j*I,(j-1)*I+1:j*I)=diag(xinom);
Q(I*J+j,I*J+J+j)=-1; 
Qij{j}=Q;
end
%l
l=[zeros(I*J+3*J+J*K+1+I,J);Gamma*eye(J);kron(eye(J),ones(I,1))];
%r
r=zeros(J,1);

The problem is with 'l', when it is zero, it works fine but when I put it as above it says that Q is not positive semi-definite.

Can anyone help me?

Thanks

[Urmila Rajpurohith]

Hi Nazanin

Can you provide the values of J,K,xinom and gamma which you are using for the above case.

[Nazanin Madani]

Hello Urmila,

I=10, J=5, Gamma=8.2456, and xinom=[49 29 23 40 18 17 48 13 15 31].

[Urmila Rajpurohith]

Provide K value.

[Nazanin Madani]

K=286

Answer 1

[Urmila Rajpurohith]

You mentioned that your code is working fine for I=0 but when I tried with I=0, I got the error:

Unable to perform assignment because the size of the left side is 0-by-0 and the size of the right side is 10-by-10

for the line:

Q((j-1)*I+1:j*I,(j-1)*I+1:j*I)=diag(xinom);

When I is not equal to 0, the determination of positive definiteness depends on the values provided as input. Try manually checking whether the matrix you obtain is positive semi definite or not.

[Nazanin Madani]

Hi, thank you for your reply. I was talking about

l=[zeros(I*J+3*J+J*K+1+I,J);Gamma*eye(J);kron(eye(J),ones(I,1))];

which indicates the small L in the SOC constraint, I should have been more clear.