About using SOCP solvers to solve QCQP

2022-03-29

An answer to this question on the Scientific Computing Stack Exchange.

Question

I have noticed that some commercial solvers transform QCQPs into SOCPs and use SOCP algorithms to solve the resulting problem. I am wondering if there is a benefit to this approach over using a pure QCQP solver.

I have done some literature review, and I haven't found any references comparing these two approaches, besides some claims from MOSEK, SOCP solvers are more robust.

Does anyone know any references on this topic?

I appreciate the help.

Answer

Since QCQP is contained within SOCP you don't lose any expressiveness by making this transformation. However, you do reduce the maintenance cost of the software! If the accuracy+perf difference is small enough, that's a compelling reason.