Optimization models and methods I

LINMA1702  2019-2020  Louvain-la-Neuve

Optimization models and methods I
5.0 credits
30.0 h + 22.5 h
2q

Teacher(s)
Language
Français
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)

Program title
Sigle
Credits
Prerequisites
Aims
Master [120] in Computer Science
5
-

Minor in Applied Mathematics
5
-

Master [120] in Chemical and Materials Engineering
5
-

Master [120] in Electrical Engineering
5
-

Master [120] in Computer Science and Engineering
5
-

Additional module in computer science
5
-

5
-

Minor in Engineering Sciences: Applied Mathematics (only available for reenrolment)
5
-

Bachelor in Mathematics
5
-

Additionnal module in Mathematics
5
-

Specialization track in Applied Mathematics
5
-