This can be formulated as an SOCP. norm(x-a(:,i)) <= sqrt(k(i)) . But CVX will convert the SDP into an SOCP (but maybe with norrm squared), so it might be a little better to directly enter it as an SOCP.
Thank you. I have tried using SOCP format. However, SDP format takes less time to execute than the SOCP format. Other than SDP/SOCP can it be solved by any other technique that is fast enough?