Biggest conic quadratic problem solved by MOSEK ever

Recently we got a bug report from a customer. The reason for the bug was that the problem has more than 2^31 nonzeros in the A matrix so a 32 bit integer overflow triggered an assert.

After fixing the bug the problem was not solvable on the largest computer which we had access to. After buying a new DELL PowerEdge R730 server with 2 Xeon E5-2687W v4 3.0GHZ  and 512GB the problem solved in about 2000 seconds using 24 threads using the latest MOSEK version 8.0.0.74.

Here are the size details about the problem:

• Number linear constraints: 140623
• Number of variables: 545634
• Number conic constraints: 124801
• Number of nonzeros in A: 2208749451 (>2^31)
• Number of flops per iteration: 10^13

Because the bug discussed above is present in all previous versions of MOSEK then this is the biggest problem in terms of A nonzeros solved by MOSEK ever.