Second Level Degree in Mathematics
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OPTIMIZATION - 6 CFU
Teacher
Scheduled Period
I Year - 2 Semester | 28/02/2022 - 11/06/2022
Hours: 48 (48 lezione)
Prerequisites
Linear programming.
Target skills and knowledge
Knowledge in constrained optimzation, with emphasis on Integer linear programming.
Examination methods
Written exam.
Assessment criteria
Students are expected to achieve a full understanding of the theoretical notions presented in this course and to be able to use this knowledge to solve problems.
Course contents
Polyhedra and linear inequalities:
- Fourier's method;
- Minkowski-Weyl's theorem;
- recession cone;
- faces and unicity of the representation;
- projections.
Ideal formulations:
- total unimodularity;
- directed graphs, flows and paths;
- matchings;
- minimum spanning trees;
- Meyer's theorem;
- union of polyhedra.
Valid inequalities for integer programs;
- Chvátal-Gomory inequalities;
- split inequalities.
Planned learning activities and teaching methods
Lessons and exercises.