Burer has shown that completely positive relaxations of nonconvex quadratic programs with nonnegative and binary variables are exact when the binary variables satisfy a so-called key assumption. Here we show that introducing binary variables to obtain an equivalent problem that satisfies the key assumption will not improve the semidefinite relaxation, and only marginally improve the doubly nonnegative relaxation.

## Citation

Technical report, Mathematisches Institut, Heinrich-Heine-UniversitÃ¤t DÃ¼sseldorf, http://www.opt.uni-duesseldorf.de/~jarre/papers/2744.pdf