A note on representations of linear inequalities in non-convex mixed-integer quadratic programs

In the literature on the quadratic 0-1 knapsack problem, several alternative ways have been given to represent the knapsack constraint in the quadratic space. We extend this work by constructing analogous representations for arbitrary linear inequalities for arbitrary nonconvex mixed-integer quadratic programs with bounded variables.

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Gap inequalities for non-convex mixed-integer quadratic programs

Laurent and Poljak introduced a very general class of valid linear inequalities, called gap inequalities, for the max-cut problem. We show that an analogous class of inequalities can be defined for general nonconvex mixed-integer quadratic programs. These inequalities dominate some inequalities arising from a natural semidefinite relaxation.

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Inequalities for Mixed Integer Linear Programs

This tutorial presents a theory of valid inequalities for mixed integer linear sets. It introduces the necessary tools from polyhedral theory and gives a geometric understanding of several classical families of valid inequalities such as lift-and-project cuts, Gomory mixed integer cuts, mixed integer rounding cuts, split cuts and intersection cuts, and it reveals the relationships between these...

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Valid inequalities for mixed integer linear programs

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Unbounded convex sets for non-convex mixed-integer quadratic programming

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A note on representations of linear inequalities in non-convex mixed-integer quadratic programs

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