Improved row-by-row method for binary quadratic optimization problems
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The research presented here is an improved row-by-row (RBR) algorithm for the solution of boolean quadratic programming (BQP) problems. While a faster and implementable RBR method has been widely used for semidefinite programming (SDP) relaxed BQPs, it can be challenged by SDP relaxations because of the fact that it produce a tighter lower bounds than RBR on BQPs. On the other hand, solving SDP by interior point method (IPM) is computationally expensive for large scale problems. Departing from IPM, our methods provides better lower bound than the RBR algorithm by Wai et al. (IEEE international conference on acoustics, speech and signal processing ICASSP, 2011) and competitive with SDP solved by IPM. The method includes the SDP cut relaxation on the SDP and is solved by a modified RBR method. The algorithm has been tested on MATLAB platform and applied to several BQPs from BQPLIB (a library by the authors). Numerical experiments show that the proposed method outperform the previous RBR method proposed by several authors and the solution of BQP by IPM as well.
KeywordsUnconstrained quadratic binary optimization Row-by-row method Semidefinite programming Computer vision First order method
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