EduXchange.EU

POLYHEDRAL METHODS FOR INTEGER PROGRAMMING

96351
Computer Science and ICT, Data, AI

Over deze cursus

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.

Leerresultaten

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.

Veronderstelde voorkennis

Basic knowledge of linear programming

Activiteiten

Attending virtual lectures and submitting homework assignment via electronic form

Aanvullende informatie

  • Studiepunten
    ECTS 2.5
  • Niveau
    Master
  • Contact uren per week
    3
  • Instructeurs
    Asaf Levin
Als er nog iets onduidelijk is, kijk even naar de FAQ van Technion (Israel).

Aanbod

  • Startdatum

    27 mei 2024

    • Einddatum
      22 augustus 2024
    • Periode *
      Spring Semester 2023/24
    • Locatie
      Haifa
    • Voertaal
      Engels
    Inschrijvingsperiode gesloten
Dit aanbod is voor studenten van TUM (Germany)