Optimization models and methods
[INMA2471]
[30h + 22.5h] 5 credits
This course is taught in the 1st semester.
Teacher(s): François Glineur
Language: French
Level: Second
Aims
Main themes
2. Introduction to three categories of problems : linear optimization, convex optimization and nonlinear optimization ; for each of them :
a.What problems can we formulate ?
(presentation of the class of problems that can be modelled)
b.How can we solve them ?
(description and analysis of relevant solving techniques)
3.Modelling and practical resolution of real-world problems using a modelling language and/or specialized software.
Content and teaching methods
1. Optimization models
Linear optimization and duality.
Convex optimization, duality and conic formulation.
Nonlinear optimization and optimality conditions.
2. Optimization methods
Interior-point methods for linear optimization, conic optimization (quadratic and semidefinite) and convex optimization ; algorithmic complexity.
Trust-region methods and Nelder-Mead method for nonlinear optimization.
Exercises and projects
Formulation and resolution of concrete problems.
AMPL modelling language.
Other information (prerequisite, evaluation (assessment methods), course materials recommended readings, ...)
Basic notions of real calculus, linear algebra and basic notions in optimization (material from the course INMA 2702)
Evaluation :
Group projects during the semester and final written exam ; course material available on the icampus web site.