Dynamically generated cutting planes for mixed-integer quadratically constrained quadratic programs and their incorporation into GloMIQO 2
Christodoulos A. Floudas
Ruth Misener
James B. Smadbeck
10.6084/m9.figshare.1310478.v1
https://tandf.figshare.com/articles/journal_contribution/Dynamically_generated_cutting_planes_for_mixed_integer_quadratically_constrained_quadratic_programs_and_their_incorporation_into_GloMIQO_2/1310478
<div><p>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 [<i>Concave extensions for nonlinear 0-1 maximization problems</i>, 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.</p></div>
2015-01-02 00:00:00
program
bb
paper documents
framework
equation
Novel contributions
multivariable terms
GloMIQO 2.
algorithmic descriptions
GloMIQO 2
termwise relaxation
nonlinear terms
quadratically
MIQCQP
Computational results
GloMIQO 2 performance
Concave extensions