Foundations of Distributed and Large Scale Computing Optimization

  • Emilie CHOUZENOUX, LIGM, Univ. Paris Est
  • Jean-Christophe PESQUET, LIGM, Univ. Paris Est

    In a wide range of application fields (inverse problems, machine learning, computer vision, data analysis, networking,...), large scale optimization problems need to be solved.

    The objective of this course is to introduce the theoretical background which makes it possible to develop efficient algorithms to successfully address these problems by taking advantage of modern multicore or distributed computing archtectures. This course will be mainly focused on nonlinear optimization tools for dealing with convex problems. Proximal tools, splitting techniques and Majorization-Minimization strategies which are now very popular for processing massive datasets will be presented. Illustrations of these methods on various applicative examples will be provided.

    Course outline. The course consists of eight sessions (3h each) combining lectures and exercices. The following concepts will be presented:

    1. Introduction to optimization problems

    2. Background on convex analysis

    3. Parallel proximal splitting methods

    4. Majorization-Minimization approaches

    5. Stochastic methods