Aims

Learn how to formulate, analyze and solve optimization problems.

Main themes

1. Basic concepts and classification of optimization problems.

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

Course
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, ...)

Prerequisites :
Basic notions of real calculus, linear algebra and matrix theory (course INMA2702 is not a prerequisite).

Evaluation :
Group projects during the semester and final written exam ; course material available on the icampus web site.

Programmes in which this activity is taught

Other credits in programs