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
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

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

Title of the programme
Mineure en Mathématiques appliquées

Master [120] : ingénieur civil en informatique

Master [120] en sciences informatiques

Master [120] : ingénieur civil électricien

Master [120] : ingénieur civil en chimie et science des matériaux

Approfondissement en sciences mathématiques

Bachelier en sciences mathématiques

Approfondissement en sciences informatiques

Mineure en sciences de l'ingénieur : mathématiques appliquées (accessible uniquement pour réinscription)

Approfondissement en statistique et sciences des données

Filière en Mathématiques Appliquées