Optimization models and methods I

linma1702  2019-2020  Louvain-la-Neuve

Optimization models and methods I
Note from June 29, 2020
Although we do not yet know how long the social distancing related to the Covid-19 pandemic will last, and regardless of the changes that had to be made in the evaluation of the June 2020 session in relation to what is provided for in this learning unit description, new learnig unit evaluation methods may still be adopted by the teachers; details of these methods have been - or will be - communicated to the students by the teachers, as soon as possible.
5 credits
30.0 h + 22.5 h
Q2
Teacher(s)
Language
French
Content
Linear optimization:
Introduction, canonical formulations, polyhedral geometry, simplex algorithm, duality et sensitivity analysis, introduction to discrete optimization (branch & bound).
Nonlinear optimization:
Models : definitions and terminology, optimality conditions for unconstrained and constrained problems ; recognize and exploit convexity of a problem.
Methods : line-search methods for unconstrained problems (gradient, Newton and quasi-Newton methods) ; convergence properties (local and global) ; implementation details ; introduction to other types of methods.
Teaching methods
This course is comprised of lectures, exercise sessions and computer labs, as well as a project to be carried out in small groups. Consulting is available for help with the project.
Evaluation methods
Students will be evaluated with an individual written exam, based on the above-mentioned objectives. Students also carry out a project in small groups, whose evaluation is taken into account for the final grade.
Online resources
Course documents (slides, notes and exercises) are available on Moodle : https://moodleucl.uclouvain.be/course/view.php?id=9200 
Bibliography
  • Introduction to Linear Optimization, Dimitri Bertsimas and John Tsitsiklis, Athena Scientific, 1997.
  • Linear Programming. Foundation and Extensions, Robert Vanderbei, Kluwer Academic Publishers, 1996.
  • Integer Programming, Laurence Wolsey, Wiley, 1998.
  • Numerical Optimization, Jorge Nocedal et Stephen J. Wright, Springer, 2006.
  • Convex Optimization, Stephen Boyd et Lieven Vandenberghe, Cambridge University Press, 2004.
Faculty or entity


Programmes / formations proposant cette unité d'enseignement (UE)

Title of the programme
Sigle
Credits
Prerequisites
Aims
Approfondissement en statistique et sciences des données

Additional module in computer science

Additionnal module in Mathematics

Minor in Engineering Sciences: Applied Mathematics (only available for reenrolment)

Master [120] in Computer Science

Specialization track in Applied Mathematics

Master [120] in Statistic: General

Minor in Applied Mathematics

Master [120] in Computer Science and Engineering

Master [120] in Chemical and Materials Engineering

Bachelor in Mathematics

Master [120] in Electrical Engineering