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Kies de Nederlandse taal
Course module: 202300027
202300027
Linear Optimisation
Course info
Course module202300027
Credits (ECTS)5
Course typeStudy Unit
Language of instructionEnglish
Contact persondr. J. de Jong
E-mailj.dejong-3@utwente.nl
Lecturer(s)
Examiner
dr. J. de Jong
Lecturer
dr. J. de Jong
Contactperson for the course
dr. J. de Jong
Academic year2023
Starting block
1B
RemarksPart of module 6 AM
Application procedureYou apply via OSIRIS Student
Registration using OSIRISYes
Aims
Upon completion of this course the student is able to:
  • model optimization problems as Linear Programs, and explain how these can be solved,
  • apply the simplex method,
  • apply Fourier-Motzkin Elimination,
  • construct the dual of a linear program, and use complementary slackness to compute an optimal solution to the dual, construct proofs involving convex sets, basic feasible solutions, Fourier-Motzkin Elimination, the simplex method, duality, and Farkas’ Lemma
Content
The course aims to provide an introduction to algorithmic principles and fundamental ideas of linear optimization. Optimization problems appear in many real-life situations. Examples are: How can we assign the frequencies in a wireless network such that the network is used in an optimal way?  How to choose the geometry of a design such that the device is both reliable and cheap? What is the best location for a new power plant? 

Since the 1940s linear optimization has been used in Operations Research to maximize profits in large companies. The simplex algorithm is one of the most used methods to solve linear optimization. Interestingly, it practically outperforms many algorithms that are theoretically superior. In this course, students learn how to model optimization problems as linear optimization, and how to solve these using the simplex method. But the main focus is on understanding the fundamental concepts underlying linear optimization and the simplex method, including convexity, basic feasible solutions, degeneracy, and duality. The course continues with the topic of algorithmic methods for solving linear equations and linear inequalities. The Farkas lemma provides the basis for duality results in linear optimization. Strong duality of linear optimization, sensitivity, and matrix games are treated. We then study the properties of convex sets and convex functions. These properties play an important role in optimization and applied analysis.
Module
Module 6
Participating study
Bachelor Applied Mathematics
Required materials
Book
Bertsimas, Tsitsiklis, “Introduction to Linear Optimization”. ISBN: 978-1-886529-19-9
Recommended materials
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Instructional modes
Lectorial

Recorded Lectures

Tutorial

Tests
Linear Optimisation

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Kies de Nederlandse taal