Aller au menu Aller au contenu
Our engineering & Master degrees


School of engineering in Physics, Applied Physics, Electronics & Materials
Science

Our engineering & Master degrees
Our engineering & Master degrees

> Studies

Convex Optimisation (SIGMA S9) - WPMTCOP0

A+Augmenter la taille du texteA-Réduire la taille du texteImprimer le documentEnvoyer cette page par mail cet article Facebook Twitter Linked In
  • Number of hours

    • Lectures : 10.0
    • Tutorials : 0
    • Laboratory works : 8.0
    • Projects : 0
    • Internship : 0
    ECTS : 2.0

Goals

The objective is to introduce the concepts of convex optimization and applications to inverse problems.

Contact Ronald PHLYPO

Content

This course focuses on formulating signal and image processing problems as convex optimization problems, analyzing their properties (e.g. existence and uniqueness of solutions) and designing efficient algorithms to solve them numerically. We aim at giving students the background and skills to formulate problems and use appropriate algorithms on their own applications.
Syllabus:?* Convex optimization: existence and uniqueness of solutions, subdifferential and gradient, constraints and indicator functions, monotone inclusions, nonexpansive operators and fixed point algorithms, duality, proximal operator, splitting algorithms.?* From estimation to optimization: formulating priors and constraints, regularity and parsimony, Bayesian interpretation.

  • Inverse problems: well- and ill-posed problems, data fidelity and regularization, study of signal and image recovery problems.


Prerequisites

basic analysis and linear algebra

Tests

Semester 9 - The exam is given in english only 

Lab work report * 40% + written exam * 60%



session 1 : 60% DS (oral, if applicable) + 40% CR
session 2 : 60% DS2 (oral, if applicable) + 40% CR

in case no exams can be held on site :
session 1 : 60% DS (written) + 40% CR
session 2 : 60% DS (written) + 40% CR

Additional Information

Semester 9 - This course is given in english only EN

Curriculum->Double-Diploma Engineer/Master->Semester 9
Curriculum->Master->Semester 9

Bibliography

H. H. Bauschke and P. L. Combettes, « Convex Analysis and Monotone Operator Theory in Hilbert Spaces », 2011
N. Parikh and S. Boyd, « Proximal Algorithms », Foundations and Trends in Optimization Vol. 1, No. 3 (2013) 123–231
P. L. Combettes and J.-C. Pesquet, « Proximal splitting methods in Signal Processing », chapitre de « Fixed-point algorithms for inverse problems in science and engineering », p. 185-212, 2011.

A+Augmenter la taille du texteA-Réduire la taille du texteImprimer le documentEnvoyer cette page par mail cet article Facebook Twitter Linked In

Date of update July 29, 2020

Université Grenoble Alpes