
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 FourierMotzkin 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, FourierMotzkin Elimination, the simplex method, duality, and Farkasâ€™ Lemma


The course aims to provide an introduction to algorithmic principles and fundamental ideas of linear optimization. Optimization problems appear in many reallife 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.





Bachelor Applied Mathematics 
  Required materialsBookBertsimas, Tsitsiklis, “Introduction to Linear Optimization”. ISBN: 9781886529199 

 Recommended materialsInstructional modesLectorial
 Recorded Lectures
 Tutorial

 TestsLinear Optimisation


 