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Introduction to Convex Optimization

  • Duration
    22 hours (8 lectures and 3 labs)

    Saverio Salzo – Istituto Italiano di Tecnologia -

    Silvia Villa – DIMA, Università degli Studi di Genova –
    Cesare Molinari - Istituto Italiano di Tecnologia –

    20-24 July 2020

    Convex optimization plays a key role in data sciences. The objective of this course is to provide basic tools and methods at the core of modern nonlinear convex optimization. Starting from the gradient descent method we will cover some state of the art algorithms, including proximal gradient methods, dual algorithms, stochastic gradient descent, and randomized block-coordinate descent methods.

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    Detailed Program


  • 1. Introduction

    Motivation from applications. Basic concepts: convex sets and functions.

  • 2. Smooth optimization

    General convergence principles and the gradient descent algorithm

  • 3. Lab - Gradient descent

    The gradient descent method in action

  • 4. Non smooth differential theory

  • 5. Duality theory part I

  • 6. The proximal gradient method.

  • 7. Lab - Sparsity

    Solving problems with sparsity constraints

  • 8. Proximity operators of spectral functions. Duality theory part II

  • 9. Dual algorithms and applications

  • 10. Stochastic gradient descent and randomized coordinate descent.

  • 11. Lab - Matrix completion

    Matrix completion with nuclear norm regularization and Group Lasso.