Simplified semidefinite and completely positive relaxations

This paper is concerned with completely positive and semidefinite relaxations of quadratic programs with linear constraints and binary variables as presented by Burer. It observes that all constraints of the relaxation associated with linear constraints of the original problem can be accumulated in a single linear constraint without changing the feasible set of either the completely positive or the semidefinite approximation. It also shows that a tightening of the semidefinite relaxation proposed by Burer is equivalent to the original relaxation.


Lieder, F. (2015). Simplified semidefinite and completely positive relaxations. Operations Research Letters, 43(6), 579-580.