Optimization models and methods I

linma1702  2021-2022  Louvain-la-Neuve

Optimization models and methods I
5.00 credits
30.0 h + 22.5 h

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.
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 during the second quadrimester, whose evaluation is taken into account for the final grade (one third) for each session.
  • 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
Learning outcomes
Master [120] in Chemical and Materials Engineering

Master [120] in Electrical Engineering

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

Master [120] in Computer Science and Engineering

Additional module in computer science

Bachelor in Mathematics

Approfondissement en statistique et sciences des données

Additionnal module in Mathematics

Master [120] in Computer Science

Minor in Applied Mathematics

Specialization track in Applied Mathematics