Optimization models and methods I

linma1702  2020-2021  Louvain-la-Neuve

Optimization models and methods I
Due to the COVID-19 crisis, the information below is subject to change, in particular that concerning the teaching mode (presential, distance or in a comodal or hybrid format).
5 credits
30.0 h + 22.5 h
Glineur François;
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

Due to the COVID-19 crisis, the information in this section is particularly likely to change.

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

Due to the COVID-19 crisis, the information in this section is particularly likely to change.

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 
  • 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
Force majeure
Evaluation methods
Unless only remote evaluations are allowed by the sanitary rules, the written exam is organized on site. Students unable to participate, as attested by a medical quarantine certificate, will be offered the opportunity to take the exam remotely at the same time. This parallel examination, written and proctored, will be of the same type and will cover the same topics as the main examination.

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

Title of the programme
Minor in Applied Mathematics

Master [120] in Computer Science and Engineering

Master [120] in Computer Science

Master [120] in Electrical Engineering

Master [120] in Chemical and Materials Engineering

Additionnal module in Mathematics

Bachelor in Mathematics

Additional module in computer science

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

Approfondissement en statistique et sciences des données

Specialization track in Applied Mathematics