Fiches de cours 2018-2019

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Convex optimization

MGT-418

Enseignant(s) :

Kuhn Daniel

Langue:

English

Remarque

Only in MA3

Summary

This course introduces the theory and application of modern convex optimization from an engineering perspective.

Content

Convex optimization is a fundamental branch of applied mathematics that has applications in almost all areas of engineering, the basic sciences and economics. For example, it is not possible to fully understand support vector machines in statistical learning, nodal pricing in electricity markets, the fundamental welfare theorems in economics, or Nash equilibria in two-player zero-sum games without understanding the duality theory of convex optimization.

The course primarily focuses on techniques for formulating decision problems as convex optimization models that can be solved with existing software tools. The exact formulation of an optimization model often determines whether the model can be solved within seconds or only within days, and whether it can be solved for ten variables or up to 10^6 variables. The course does not address optimization algorithms but covers the theory that is necessary to follow advanced courses on algorithm design such as EE-556: Mathematics of data: from theory to computation.

 

Tentative Course Outline:

Week 1: Introduction / Convex Sets

Week 2: Convex Sets / Convex Functions

Week 3: Convex Functions / Convex Optimization Problems

Week 4: Convex Optimization Problems

Week 5: Introduction to Duality Theory

Week 6: Optimality Conditions / Separation Theorems

Week 7: Strong Duality

Week 8: Optimization in Statistics and Machine Learning

Week 9: Optimization in Statistics and Machine Learning

Week 10: Convexifying Nonconvex Problems

Week 11: Convexifying Nonconvex Problems

Week 12: Robust Optimization

Week 13: Robust Optimization

Week 14: Stochastic Programming

Learning Prerequisites

Required courses

Students are assumed to have good knowledge of linear algebra and analysis.

Important concepts to start the course

Some familiarity with linear programming or other optimization paradigms is useful but not necessary. Students are expected to be familiar with the MATLAB programming environment.

Learning Outcomes

By the end of the course, the student must be able to:

Teaching methods

Classical formal teaching interlaced with practical exercices and computational courseworks.

Assessment methods

Midterm Exam (30%, covering weeks 1-7)

3 MATLAB-based Courseworks (20%, covering weeks 8-14)

Final Exam (50%, covering weeks 1-14)

Supervision

Office hours Yes
Assistants Yes
Forum No

Resources

Bibliography

Ressources en bibliothèque

Dans les plans d'études

Semaine de référence

 LuMaMeJeVe
8-9     
9-10     
10-11   INM10 
11-12    
12-13     
13-14     
14-15   BC03 
15-16    
16-17     
17-18     
18-19     
19-20     
20-21     
21-22     
 
      Cours
      Exercice, TP
      Projet, autre

légende

  • Semestre d'automne
  • Session d'hiver
  • Semestre de printemps
  • Session d'été
  • Cours en français
  • Cours en anglais
  • Cours en allemand