Ensimag Rubrique Formation 2022

Efficient Methods in Optimization - WMM9AM16

  • Number of hours

    • Lectures 36.0
    • Projects -
    • Tutorials -
    • Internship -
    • Laboratory works -
    • Written tests -


    ECTS 6.0


The course is meant as sequel to the course "Non-smooth convex optimization methods". It treats more advanced methods and applications of convex optimization, notably structured conic programs, their solution by interior-point methods, and reformulations or approximations of common optimization problems as conic symmetric programs.




The subject of this half-semester course are more advanced methods in convex optimization. It consists of 6 lectures, 2 x 1,5 hours each, and can be seen as continuation of the course "Non-smooth convex optimization methods". Approximate content of each lecture:

  • Linear programs / Conic programs
  • Representations of linear programs
  • Duality
  • Symmetric cones
  • Second order conic / semi-definite programming
  • Liftings / Complexity
  • Robust optimization
  • Robust counterparts of conic programs
  • Robust Linear / Second order conic / Semi-definite programs
  • Interior-point methods
  • Self-concordant barriers
  • Short / Long step path-following methods
  • Barriers for non-symmetric cones
  • Applications
  • Control problems
  • Analysis of dynamical systems
  • Topology / Shape optimization
  • Relaxations
  • MaxCut (Goemans / Williamson)
  • Stable set (Lovasz / Schrijver)
  • Copositive programming relaxations
  • Polynomial optimization
  • Sums of squares relaxations
  • Moment relaxations


Linear algebra: matrices, vector spaces, linear functions

Analysis: differentiability, gradients, convergence, continuity


The course is composed of 18 hours lectures.

Evaluation : A two-hours written exam (E1) in session 1. For those who do not pass there will be another two-hours exam (E2) in session 2.

N1 = Exam1
N2 = Exam2

The exam is given in english only FR


The course exists in the following branches:

  • Curriculum - Master in Applied Mathematics - Semester 9 (this course is given in english only EN)
see the course schedule for 2022-2023

Additional Information

Course ID : WMM9AM16
Course language(s): FR

You can find this course among all other courses.


Aharon Ben-Tal, Laurent El Ghaoui, Arkadi Nemirovski. Robust Optimization. Princeton University Press, 2009.

Aharon Ben-Tal, Arkadi Nemirovski. Lectures on Modern Convex Optimization - Analysis, Algorithms, and Engineering Applications. Vol. 2 of MPS/SIAM Series on Optimization. SIAM, 2001.

Steven Boyd, Lieven Vandenberghe. Convex Optimization. Cambridge University Press, 2004.

Jean-Bernard Lasserre. Moments, Positive Polynomials and their Applications. Vol. 1 of Imperial College Press Optimization Series. Imperial College Press, 2009.

Yurii Nesterov, Arkadi Nemirovski. Interior-Point Algorithms in Convex Programming. Vol. 13 of SIAM Stud. Appl. Math. SIAM, Philadelphia, 1994.