401-3903-11L  Geometric Integer Programming

SemesterSpring Semester 2020
LecturersJ. Paat
Periodicitynon-recurring course
Language of instructionEnglish

AbstractInteger programming is the task of minimizing a linear function over all the integer points in a polyhedron. This lecture introduces the key concepts of an algorithmic theory for solving such problems.
ObjectiveThe purpose of the lecture is to provide a geometric treatment of the theory of integer optimization.
ContentKey topics are:

- Lattice theory and the polynomial time solvability of integer optimization problems in fixed dimension.

- Structural properties of integer sets that reveal other parameters affecting the complexity of integer problems

- Duality theory for integer optimization problems from the vantage point of lattice free sets.
Lecture notesnot available, blackboard presentation
LiteratureLecture notes will be provided.

Other helpful materials include

Bertsimas, Weismantel: Optimization over Integers, 2005


Schrijver: Theory of linear and integer programming, 1986.
Prerequisites / Notice"Mathematical Optimization" (401-3901-00L)