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Home Teaching Summer Semester 2017 Convex Optimization for Machine Learning and Computer Vision (IN2330) (2h + 2h, 6 ECTS)

Convex Optimization for Machine Learning and Computer Vision (IN2330) (2h + 2h, 6 ECTS)

Many important machine learning, computer vision and image processing problems can be cast as convex energy minimization problems, e.g. training of SVMs, logistic regression, low-rank and sparse matrix decomposition, denoising, segmentation, or multiframe blind deconvolution. In this lecture we will discuss first order convex optimization methods to implement and solve the aforementioned problems efficiently. Particular attention will be paid to problems including constraints and non-differentiable terms, giving rise to methods that exploit the concept of duality such as the primal-dual hybrid gradient method or the alternating directions methods of multipliers. This lecture will cover the mathematical background needed to understand why the investigated methods converge as well as the efficient practical implementation.

We will cover the following topics:

Elements in convex analysis

  • Convex sets and functions
  • Existence and uniqueness of minimizers
  • Subdifferentials
  • Convex conjugates
  • Duality

Numerical methods

  • Gradient-based methods, Majorization-minimization algorithm, line search method
  • Proximal point algorithms, primal-dual hybrid gradient method, alternating direction method of multipliers
  • Convergence analysis
  • Preconditioning

Bilevel optimization

  • Generalized implicit function theorem
  • Adjoint approach for numerical solution

Example applications in machine learning, computer vision and signal processing, including

  • Low-rank and sparse matrix decomposition
  • Training of SVMs, Logistic regression
  • Total-variation image restoration
  • Image segmentation
  • Multiframe blind deconvolution
  • Implementation in MATLAB


Location: 02.09.023
Time and Date: Wednesday 16:15 - 18:00
Lecturer: Dr. Tao Wu
Start: April 26th, 2017
The lecture is held in English.


Location: 02.09.023
Time and Date: Monday 12:15 - 14:00
Organization: Thomas Möllenhoff, Emanuel Laude
Start: May 8th, 2017
The exercise sheets consist of two parts, theoretical and programming exercises. The upcoming exercise sheets will be passed out in the exercise class on Monday and you have one week to solve them. The solutions will be discussed in the Monday exercise class the week after. Please submit the solutions (code + theory) as a zip file with filename “” ONLY(!) containing your .pdf- and .m-files (no material files) via email to We accept both, photographs or scans of CLEAN(!) handwritten text and compiled LATEX, however we encourage you to tex your solutions. Please remember to write CLEAN(!), COMMENTED(!) code! You are allowed to work on the exercise sheets in groups of two students.

The exercise sheets can be accessed here.


By achieving at least 60% of all possible points on the exercise sheets you can obtain a bonus of 0.3 in the final exam. Note that you can neither improve a 1.0 nor a 5.0.



Lecture Material

Course material (slides and exercise sheets) can be accessed here.

Send us an email if you need the password.

Last edited 18.04.2017 13:10 by Thomas Möllenhoff