2019•FigshareOpen access

Cutting Planes and Integrality of Polyhedra: Structure and Complexity

Dabeen Lee

Abstract

In this thesis, we study theoretical aspects of integer linear programming. This thesis consists of two main parts: the first part is on the theory of cutting planes for integer linear programming, while the second part is on the theory of ideal clutters in combinatorial optimization.Cutting planes for an integer linear program are linear inequalities that are valid for all integer feasible solutions but possibly violated by some solutions to the linear programming relaxation.

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Key concepts: Integer programming, Polyhedron, Cutting-plane method, Linear programming, Integer points in convex polyhedra, Linear programming relaxation, Branch and cut, Mathematics