- General nonlinear optimization.
- Smooth and non-smooth convex optimization.
- Interior-point methods.
At the end of this learning unit, the student is able to :
- 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.
Due to the COVID-19 crisis, the information in this section is particularly likely to change.The course is given in 12-15 lectures. The computer projects are implemented by the students themselves with supporting consultations.
Due to the COVID-19 crisis, the information in this section is particularly likely to change.In the written exam (in English or French) there are four questions, one for each chapter of the course (up to 5 points for each question). The marks for the exam and the exercises are combined in the final mark.
- 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.