Friday, August 17, 2018

Solving SDP with millions of matrix variables

Is it feasible in practice to solve semidefinite optimization problems with a huge number of matrix variables?

We recently received a problem from a structural engineering application with approximately the following  parameters:

  • 1 500 000 three-dimensional matrix variables,
  • 750 000 three-dimensional rotated quadratic cones,
  • $8\cdot 10^6$ scalar variables, $15\cdot 10^6$ linear constraints, $45\cdot 10^6$ nonzeros.

On a DELL PowerEdge R730 server with 2 Xeon E5-2687W v4 3.0GHZ the optimal solution is found in about 161 minutes on 24 threads using the latest MOSEK with memory peaking at about 60GB.  Due to the nature of the problem we disabled the linear dependency check and otherwise used all standard parameter settings.