First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
MATHEMATICS
Course unit
OPTIMIZATION
SC03106405, A.A. 2018/19

Information concerning the students who enrolled in A.Y. 2018/19

Information on the course unit
Degree course Second cycle degree in
MATHEMATICS
SC1172, Degree course structure A.Y. 2011/12, A.Y. 2018/19
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Degree course track GENERALE [010PD]
Number of ECTS credits allocated 6.0
Type of assessment Mark
Course unit English denomination OPTIMIZATION
Website of the academic structure http://matematica.scienze.unipd.it/2018/laurea_magistrale
Department of reference Department of Mathematics
Mandatory attendance No
Language of instruction Italian
Branch PADOVA
Single Course unit The Course unit can be attended under the option Single Course unit attendance
Optional Course unit The Course unit can be chosen as Optional Course unit

Lecturers
Teacher in charge MICHELANGELO CONFORTI MAT/09

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Educational activities in elective or integrative disciplines MAT/09 Operational Research 3.0
Core courses MAT/09 Operational Research 3.0

Course unit organization
Period Second semester
Year 1st Year
Teaching method frontal

Type of hours Credits Teaching
hours
Hours of
Individual study
Shifts
Lecture 6.0 48 102.0 No turn

Calendar
Start of activities 25/02/2019
End of activities 14/06/2019
Show course schedule 2019/20 Reg.2011 course timetable

Examination board
Board From To Members of the board
7 Ottimizzazione - a.a. 2018/2019 01/10/2018 30/09/2019 CONFORTI MICHELANGELO (Presidente)
RINALDI FRANCESCO (Membro Effettivo)
DE FRANCESCO CARLA (Supplente)
DE GIOVANNI LUIGI (Supplente)
DI SUMMA MARCO (Supplente)

Syllabus
Prerequisites: Linear Algebra, Linear programming
Target skills and knowledge: knowledge of constrained optimization, with emphasis to Integer Programming.
Examination methods: Written exam.
Assessment criteria: Knowledge of the material presented in class, ability to develop proofs.
Course unit contents: Polyhedra and linear inequalities
Fourier's method
Farkas lemma
Theorem of Minkowski-Weyl
Recession cone
Dimension, affine hull.
Face, faces and unicity of the representation.
Projections

Ideal formulations
Total Unimodularity
Directed graphs, flows and paths.
Matchings,
Meyer's theorem.
Union of polyhedra.

Valid inequalities for Integer programs.
Chvatal-Gomory inequalities.
Split inequalities.
Planned learning activities and teaching methods: lessons and exercises presented in class.
Textbooks (and optional supplementary readings)
  • M. Conforti, G. Cornuejols, G. Zambelli, Integer Programming. New York: Springer, 2014. Cerca nel catalogo