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To cite this version:Nathan Krislock, Jérôme Malick, Frédéric Roupin. Improved semidefinite bounding procedure for solving Max-Cut problems to optimality. Mathematical Programming, Springer Verlag, 2014, 143 (1-2), pp.61-86. <10.1007/s10107-012-0594-z>. Improved semidefinite bounding procedure for solving Max-Cut problems to optimality AbstractWe present an improved algorithm for finding exact solutions to Max-Cut and the related binary quadratic programming problem, both classic problems of combinatorial optimization. The algorithm uses a branch-(and-cut-)and-bound paradigm, using standard valid inequalities and nonstandard semidefinite bounds. More specifically, we add a quadratic regularization term to the strengthened semidefinite relaxation in order to use a quasi-Newton method to compute the bounds. The ratio of the tightness of the bounds to the time required to compute them can be controlled by two real parameters; we show how adjusting these parameters and the set of strengthening inequalities gives us a very efficient bounding procedure. Embedding our bounding procedure in a generic branch-and-bound platform, we get a competitive algorithm: extensive experiments show that our algorithm dominates the best existing method.