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Convex Hulls for Non-Convex Mixed-Integer Quadratic Programs with Bounded Variables

Laura Galli(laura.galli***at***unipi.it)
Adam N. Letchford(a.n.letchford***at***lancaster.ac.uk)

Abstract: We consider non-convex mixed-integer quadratic programs in which all variables are explicitly bounded. Many exact methods for such problems use additional variables, representing products of pairs of original variables. We study the convex hull of feasible solutions in this extended space. Some other approaches use bit representation to convert bounded integer variables into binary variables. We study the convex hulls associated with some of these formulations as well. We also present extensive computational results.

Keywords: mixed-integer nonlinear programming; global optimisation; polyhedral combinatorics

Category 1: Integer Programming ((Mixed) Integer Nonlinear Programming )

Category 2: Integer Programming (Cutting Plane Approaches )

Category 3: Combinatorial Optimization (Polyhedra )

Citation: Working paper, Department of Management Science, Lancaster University, UK.

Download: [PDF]

Entry Submitted: 12/19/2019
Entry Accepted: 12/20/2019
Entry Last Modified: 12/19/2019

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