Optimization : Nonlinear programming

linma2460  2025-2026  Louvain-la-Neuve

Optimization : Nonlinear programming
5.00 credits
30.0 h + 22.5 h
Q2
> Schedule
Teacher(s)
Nunes Grapiglia Geovani;
Language
English
> French-friendly
Prerequisites
Basic knowledge of Nonlinear Analysis and Linear Algebra.
The target audience is the students interested in scientific computing, machine learning and optimization in engineering.
Main themes
  • General nonlinear optimization.
  • Smooth and non-smooth convex optimization.
  • Interior-point methods.
Learning outcomes

At the end of this learning unit, the student is able to :

Learning outcomes:
  • AA1.1, AA1.2, AA1.3
  • AA2.1
  • AA5.2, AA5.3
After this course, the student will be able to :
  • estimate the actual complexity of Nonlinear Optimization problems;
  • apply lower complexity bounds, which establish the limits of performance of optimization method;
  • explain the main principles for constructing the optimal methods for solving different types of minimization problems;
  • use the main problem classes (general nonlinear problems, smooth convex problems, nonsmooth convex problems, structural optimization ' polynomial-time interior-point methods);
  • understand the rate of convergence of the main optimization methods;
  • two testing computer projects give a possibility to compare the theoretical conclusions and predictions with real performance of minimization methods.
Additional benefits :
  • Training in scientific English.
  • Experience in solving difficult nonlinear optimization problems.
 
Content
  • General problem of nonlinear optimization. Black-box concept. Iterative methods and analytical complexity. Gradient method and Newton method. Local complexity analysis.
  • Convex optimization: convex sets and functions; minimization of differentiable and non-differentiable convex functions; lower complexity bounds; optimal methods.
  • Interior-point methods: notion of self-concordant functions and barriers; path-following methods; structural optimization.
Teaching methods
The course is given in 12-15 lectures. The computer projects are implemented by the students themselves with supporting consultations.
Evaluation methods
A written exam will count for 75% of the grade. The remaining 25% are obtained through one homework.
Online resources
https://moodle.uclouvain.be/course/view.php?id=5537
The full syllabus (in English) can be downloaded from the web page of the course.
Bibliography
  • Yu.Nesterov. "Introductory lectures on convex optimization. Basic course", Kluwer 2004
  • P. Polyak, « Introduction in optimization », J. Willey & Sons, 1989
  • Yu. Nesterov, A. Nemirovsky, « Interior-point polynomial algorithms in nonlinear optimization », SIAM, Philadelphia, 1994.
Faculty or entity
> MAP


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

Title of the programme
Sigle
Credits
Prerequisites
Learning outcomes
Master [120] in Mathematical Engineering
MAP2M
5
Master [120] in Data Science Engineering
DATE2M
5
Master [120] in Data Science: Information Technology
DATI2M
5