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Teaching

Master ACSYON: Algorithmique, Calcul Symbolique et Optimisation Numérique

  1. Fast Algorithmic Methods for Optimization and Learning (Master 2)

    This course introduces fast first-order algorithms for large-scale optimization and learning. It covers ISTA and FISTA for linear inverse problems, their convergence properties and their links with Nesterov acceleration. A continuous-time viewpoint is used to derive inertial methods, Hessian-driven damping and asymptotically vanishing damping. Applications include image denoising, deconvolution, inpainting, motion estimation and segmentation.

    Prerequisites: Linear algebra, topology and differential calculus in Rn, convex analysis, and basic optimization.

    Keywords: First-order optimization algorithms, ISTA, FISTA, Nesterov acceleration, damped inertial gradient methods, Hessian-driven damping algorithms, asymptotically vanishing damping.

  2. Nonsmooth Dynamical Systems (Master 2 ACSYON)

    This course presents mathematical and numerical tools for nonsmooth dynamical systems arising in mechanics and electrical circuits. It covers differential and Filippov inclusions, linear complementarity systems, evolution variational inequalities and Moreau’s sweeping process. Particular attention is given to existence and uniqueness, time-discretization schemes and simulations with SICONOS.

    Prerequisites: Linear algebra, ordinary differential equations, convex analysis, and basic numerical analysis.

    Keywords: Nonsmooth dynamics, differential inclusions, complementarity systems, sweeping processes, numerical schemes, SICONOS.

  3. Numerical Optimization (Master 2 ACSYON)

    This course covers the theory and implementation of numerical methods for constrained and unconstrained nonlinear optimization. It introduces line-search and trust-region strategies, conjugate-gradient, Newton and quasi-Newton methods, as well as linear and quadratic programming, penalty and augmented Lagrangian techniques, sequential quadratic programming and interior-point methods. Practical sessions use MATLAB and AMPL.

    Prerequisites: Linear algebra, differential calculus in Rn, and basic optimization.

    Keywords: Nonlinear optimization, line search, trust regions, Newton methods, quadratic programming, interior-point methods.

  4. Foundations of Optimization (Master 1 ACSYON)

    This introductory course presents the main classes of optimization problems: linear and nonlinear, continuous and discrete, constrained and unconstrained, local and global, convex and nonconvex, deterministic and stochastic. It develops first-order optimality and Karush–Kuhn–Tucker conditions, Lagrangian duality, complementarity problems and sensitivity analysis.

    Prerequisites: Linear algebra, differential calculus and topology in finite-dimensional spaces.

    Keywords: Unconstrained optimization, constrained optimization, optimality conditions, Lagrangian, duality.

  5. Introduction to Machine Learning (Master 1 ACSYON)

    This course introduces the fundamental concepts and algorithms of machine learning. It explains how quantitative models learn from data and focuses on statistical learning models and the optimization algorithms used to train them. Applications include search engines, image and speech recognition, social networks, autonomous vehicles and medical diagnosis.

    Prerequisites: Linear algebra, topology and differential calculus in Rn, probability and statistics.

    Keywords: Supervised learning, nearest-neighbor methods, support vector machines, artificial neural networks.

  6. Convex Analysis (Master 1 ACSYON)

    This course introduces the fundamental tools of finite-dimensional convex analysis and their role in optimization. It studies convex sets and functions in Rn, their topological properties and the separation of convex sets. These concepts provide the theoretical foundations required for continuous and numerical optimization.

    Prerequisites: Linear algebra, topology and differential calculus in Rn.

    Keywords: Convex sets, convex functions, separation theorems, finite-dimensional convex analysis, optimization.

  7. Stability of Dynamical Systems (Master 1 ACSYON)

    This course presents the mathematical tools used to analyse the stability of nonlinear dynamical systems governed by ordinary differential equations. It develops Lyapunov stability, invariance principles, attractivity and asymptotic behaviour, with applications in control theory, electronics, mechanics and biology.

    Prerequisites: Linear algebra, differential calculus and ordinary differential equations.

    Keywords: Dynamical systems, Lyapunov stability, invariance principles, attractivity, nonlinear systems, control theory.