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|Abstract:||The global mixed-integer quadratic optimizer, GloMIQO, addresses mixed-integer quadratically constrained quadratic programs (MIQCQP) to ε-global optimality. This paper documents the branch-and-cut framework integrated into GloMIQO 2. Cutting planes are derived from reformulation–linearization technique equations, convex multivariable terms, αBB convexifications, and low- and high-dimensional edge-concave aggregations. Cuts are based on both individual equations and collections of nonlinear terms in MIQCQP. Novel contributions of this paper include: development of a corollary to Crama's [Concave extensions for nonlinear 0-1 maximization problems, Math. Program. 61 (1993), pp. 53–60] necessary and sufficient condition for the existence of a cut dominating the termwise relaxation of a bilinear expression; algorithmic descriptions for deriving each class of cut; presentation of a branch-and-cut framework integrating the cuts. Computational results are presented along with comparison of the GloMIQO 2 performance to several state-of-the-art solvers.|
|Citation:||Misener, Ruth, James B. Smadbeck, and Christodoulos A. Floudas. "Dynamically generated cutting planes for mixed-integer quadratically constrained quadratic programs and their incorporation into GloMIQO 2." Optimization Methods and Software 30, no. 1 (2015): 215-249. doi: 10.1080/10556788.2014.916287|
|Pages:||215 - 249|
|Type of Material:||Journal Article|
|Journal/Proceeding Title:||Optimization Methods and Software|
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