Integer Programming
The course will provide a comprehensive treatment of integer optimization, including theory, algorithms, and applications at the introductory graduate level. Some specific topics to be covered are: Polyhedral Theory, Relaxations, Integral Polyhedra, Matroids, Submodular Functions, Dynamic Programming, Primal and Primal-Dual Techniques, Branch & Bound, Cutting Planes, Lagrangian Duality.Mathematical maturity at the level of a beginning graduate student (ability to understand and write proofs) will be assumed. Familiarity with reading and writing mathematical proofs (e.g., proofs by induction and contradiction) and basic knowledge in Linear Algebra are required. Prior coursework in Linear Programming and Graph Theory will be helpful.