186.835 Mathematical Programming
Diese Lehrveranstaltung ist in allen zugeordneten Curricula Teil der STEOP.
Diese Lehrveranstaltung ist in mindestens einem zugeordneten Curriculum Teil der STEOP.

2024S, VU, 2.0h, 3.0EC

Merkmale

  • Semesterwochenstunden: 2.0
  • ECTS: 3.0
  • Typ: VU Vorlesung mit Übung
  • Format der Abhaltung: Hybrid

Lernergebnisse

Nach positiver Absolvierung der Lehrveranstaltung sind Studierende in der Lage...

  • overview the area of mathematical optimization with focus on mixed integer linear programming (MIP),
  • model both academic and real world decision problems as MIPs,
  • theoretically analyze and compare different MIP formulations for a problem,
  • understand common methodology for solving MIPs,
  • develop practical solution algorithms using state-of-the-art MIP frameworks.

Inhalt der Lehrveranstaltung

  • Overview on mathematical optimization (focus on mixed integer linear models, but also discussing non-deterministic models)
  • Modeling (real world) problems as MIPs (basic techniques, modeling with exponentially many constraints and/or variables)
  • Solution methods for MIPs
    - Cutting plane method, branch-and-cut
    - Decomposition approaches (Lagrangian decomposition, Dantzig-Wolfe decomposition) and corresponding solution methods (subgradient method, column generation, branch-and-price)
  • Theory of valid inequalities and further theoretical concepts
    - (Strong) valid inequalities (Chvatal-Gomory cuts, Gomory cuts, cover cuts, theoretical concepts such as dominance, redundancy, facet-defining cuts)
    - "Well-solved" problems (properties, total unimodularity, optimization = separation)
  • Stochastic and robust optimization
  • Further issues in MIP computation and components of modern MIP solvers (presolving, primal heuristics, symmetry, frameworks)

Methoden

 

  • Lecture (attendance optional - recordings from previous years available)
  • Introduction to the usage of state-of-the-art MIP solver frameworks (Gurobi, CPLEX)
  • Homework exercises
  • Programming exercises

Prüfungsmodus

Prüfungsimmanent

Weitere Informationen

Estimated effort:

Hours | Purpose
20       | Lecture
15       | Homework exercises 
25       | Programming exercise
15       | Exam preparation and exam
--------------------------------------
75       | Overall

Vortragende Personen

Institut

Leistungsnachweis

  • Homework exercises (max. 20 points): Exercises are done at home and solutions are uploaded in TUWEL.
  • Programming Exercises (max. 40 points): Different MIP formulations for a specified optimization problem are designed and implemented. You can (optionally) join in groups of two. Your solutions are uploaded in TUWEL.
  • Written exam (max. 40 points)

Grading

The grade you receive depends on the total points collected for all tasks, but you need at least 30 points in the exercise part (including homework and programming exercises) and at least 20 points in the written exam to get a positive grade. The final grade is obtained by the following mapping:

1: 88 - 100 points
2: 75 - 87.5
3: 63 - 74.5
4: 50 - 62.5
5: 0 - 49.5

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Curricula

StudienkennzahlVerbindlichkeitSemesterAnm.Bed.Info
066 504 Masterstudium Embedded Systems Keine Angabe
066 645 Data Science Keine Angabe
066 646 Computational Science and Engineering Keine Angabe
066 926 Business Informatics Gebundenes Wahlfach
066 931 Logic and Computation Gebundenes Wahlfach
066 932 Visual Computing Gebundenes Wahlfach
066 937 Software Engineering & Internet Computing Gebundenes Wahlfach

Literatur

all material is available in TUWEL

Vorkenntnisse

  • Basic knowledge of (integer) linear programming (modeling, LP based Branch-and-Bound), e.g., as taught in Algorithmics
  • Knowledge of basic algorithms and data structures
  • Programming skills in some language, e.g., Java, C++, Python
  • Basic knowledge of linear algebra and graph theory

Vorausgehende Lehrveranstaltungen

Begleitende Lehrveranstaltungen

Sprache

Englisch