Optimization models and methods I

Teacher(s)

Glineur François;

Language

French

Prerequisites

The prerequisite(s) for this Teaching Unit (Unité d’enseignement – UE) for the programmes/courses that offer this Teaching Unit are specified at the end of this sheet.

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 methods (conjugate gradient, constrained problems, unavailable derivatives).

Teaching methods

The 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

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

MAP