Course: control and dynamical system tools for optimisation


Everything you wanted to know and you never dared to ask at the intersection on control theory, dynamical systems, and optimisation. For instance: is optimisation just a feedback loop on a system with a static non-linearity?

A series of 3 seminars at the M2/PhD level (but also good for researchers working in related fields) on one of the latest trends in optimisation! Sponsored by the ANR and hosted at ENSTA.

Introduction

We have seen a recent interest in using control tools to understand and design optimisation algorithms. The celebrated Lessard et al. paper framing optimisation algorithm design as a control problem is an example. In this course, we introduce the needed control tools and show how they can be used to interpret optimisation algorithms and their acceleration as the control of Lur'e systems. This way of approaching the problem gives us insights and more flexibility.

Speaker

Prof. Ivano Notarnicola, University of Bologna. Ivano is visiting us, you can book time to discuss with him!

Location

ENSTA, Institut Polytecnique de Paris. Inscription is free but mandatory if you are coming from outside the Institut Polytechnique de Paris. Send an email to andrea.simonetto@ensta.fr .

Schedule: attention change to the afternoon!

Subscribe and add it to your calendar: [get course-calendar.ics]

  • Monday 26/01, 14h00-16h00. Introduction to discrete-time system theory [All you need to start] [Slides]
  • Monday 02/02, 14h00-16h00. The gradient method analysis via control tools [The basic results for gradient] [Slides]
  • Monday 09/02, 14h00-16h00. Integral control for (seemingly) diverse problems [Acceleration and Nesterov's] [Slides]

Room: 2.2.34 (second floor, second wing, room 34) Change of room.

Sample references

  • L Lessard, B Recht, A Packard, Analysis and Design of Optimization Algorithms via Integral Quadratic Constraints, SIOPT, 2016
  • M Bin, I Notarnicola, T Parisini, Semiglobal exponential stability of the discrete-time Arrow-Hurwicz-Uzawa primal-dual algorithm for constrained optimization, Math Prog, 2024
  • I Notarnicola, M Bin, L Marconi, G Notarstefano, The gradient tracking is a distributed integral action, IEEE TAC, 2023
  • I Notarnicola, A Falsone, Passivity-based analysis of the ADMM algorithm for constraint-coupled optimization, Automatica, 2022