POLYHEDRAL METHODS FOR INTEGER PROGRAMMING

formulation of integer programming problems, polyhedral structures, integrality of polyhedrons, facets defining inequalities, efficiency of algorithms, complexity theory, solution methods for integer programming problems cutting planes, column generation, branch and bound, lagrangian duality, dynamic programming, heuristics. algorithms. learning outcomes at the end of the course the student will

1. understand the quality of different modeling of integer programming problems.
2. understand the definition of a polyhedron and its algebraic properties.
3. be able to solve integer programing problems with various solution methods.

At the end of the course the student will accomplish the following:

1. To formulate combinatorial optimization problems as integer (linear) programs.
2. To understand definitions related to polyhedral theory of integer programming.
3. To prove and use the integrality properties of polytopes defined using constraint matrices satisfying the definitions of TDI matrices, network matrices, totally unimodular matrices, balanced matrices, totally balanced matrices, and perfect graphs.
4. To prove that a given inequality for a new optimization problem is a valid inequality or strong valid inequality.
5. To compute the dimension of a face (for a given polytope).
6. To understand and use different notions of duality for integer programming.
7. To use general purpose algorithms like Branch and Bound, Cutting planes, Column generation and their mixtures.

Basic knowledge of linear programming

Attending virtual lectures and submitting homework assignment via electronic form