Memory Consumption of Semidefinite Programming

Hi Guys here:
Has memory consumption of CVX ever been a problem to you? Recently I wanted to solve a 1000X1000 semidefinite programming using CVX, however my computer could not bear that. My computer only has 6GB RAM and as a matter of fact it can only calculate semidefinite programming with 400X400 scale. Could anyone give any advise? Thank you!

Yes, that can indeed be a large problem by CVX standards. A 500,000 variable problem is certainly doable, or even larger—I just solved a 1,000,000-variable SOCP the other day with very little difficulty. But LMIs are among the most complex and memory-intensive, so SDPs tend to consume more memory than similarly-sized LPs and SOCPs.

You may have limited success by calling an underlying solver directly, but more likely you will need to use solvers carefully designed for larger-scale problems like CSDP or SDPA, or perhaps even a custom algorithm.