Bounds and fast approximation algorithms for binary quadratic optimization problems with application to MAX 2SAT Original Research Article

We consider binary convex quadratic optimization problems, particularly those arising from reformulations of well-known combinatorial optimization problems such as MAX 2SAT (and MAX CUT). A bounding and approximation technique is developed. This technique subsumes the spherical relaxation, while it can also be considered as a restricted variant of the semidefinite relaxation. Its complexity however is comparable to that of the first. It is shown how the quality of the obtained approximate solution can be measured. We conclude with extensive computational results on the MAX 2SAT problem, which show that good-quality solutions are obtained.