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We propose a method for low-rank semidefinite programming in application tothe semidefinite relaxation of unconstrained binary quadratic problems. Themethod improves an existing solution of the semidefinite programming relaxationto achieve a lower rank solution. This procedure is computationally efficientas it does not require projecting on the cone of positive-semidefinitematrices. Its performance in terms of objective improvement and rank reductionis tested over multiple graphs of large-scale Gset graph collection and overbinary optimization problems from the Biq Mac collection.

Efficient Rank Minimization to Tighten Semidefinite Programming for Unconstrained Binary Quadratic Optimization