Optimization models and methods I

Teacher(s)

Glineur François;

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 are assessed individually with a written exam organized during the session, based on the learning outcomes listed above. In addition, students complete a project in small groups during the second term. The grade of the project is acquired for all the sessions of the academic year (it is not possible to redo the project in the second session). 
The final grade is awarded on the basis of the project (6 points out of 20) and the exam (14 points out of 20).
All external sources of information used in the writing of assignments must be cited in accordance with bibliographic referencing standards. The use of generative artificial intelligence is permitted, but must be clearly indicated (specify concerned passages and usage, e.g. information retrieval, text drafting, text correction). Authors remain responsible for the content of their work.

Online resources

https://moodle.uclouvain.be/course/view.php?id=2039

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.

Teaching materials

• Transparents du cours sur Moodle
• Syllabus d'exercices et laboratoires sur Moodle
• Recueil d'anciens examens fourni sur Moodle

Faculty or entity

> MAP