Convex relaxations of non-convex mixed integer quadratically constrained programs: extended formulations

Convex relaxations of non-convex mixed integer quadratically constrained programs: projected formulations

“…In addition to the cut generators described in the previous sections, we also used the Cut Generating Linear Programming (CGLP) framework described in our companion paper [17] (also see [2]) to derive disjunctive cuts. Recall that the CGLP framework requires a polyhedral relaxation of MIQCP and a class of disjunctions that is satisfied by every feasible solution to the problem.…”

“…Our computational results have two highlights. First, on the GLOBALLib instances we are able to generate relaxations that are almost as strong as those proposed in [17] even though our computing times are about 100 times smaller, on average. Second, on the box QP instances the strengthened relaxations generated by our code are almost as strong as the MIQCP-SDP relaxation and can be solved in less than 2 sec even for larger instances with 100 variables; the MIQCP-SDP relaxations of the same set of instances can take up to a couple of hours to solve using a state-of-the-art SDP solver.…”

“…Such convex quadratic cuts might arise, for instance, while strengthening the extended formulation of MIQCP (see [16,17]). …”

“…MIQCP-SDP has been extensively studied in the past one decade and good progress, both theoretical and computational, has been made. In our companion paper [17] we investigate further strengthening of MIQCP-SDP relaxation using disjunctive cuts and report promising computational results. Despite these early successes, the presence of an enormous number O(n 2 ) of additional Y ij variables continues to haunt researchers pursuing this line of research.…”

“…These experiments were conducted on a test bed comprising instances from GLOBALLib [9], instances from Lee and Grossmann [11], and Box-QP instances from [22]. Besides reporting the strengths of various relaxations examined in this paper, we also study the marginal impact of various classes of cutting planes and compare our results with those presented in our companion paper [17]. Our computational results have two highlights.…”