The exam will take place in the Lecture Hall 2 (HS2) in the Physics building (Kirchhoff-Institut für Physik, KIP, INF 227) on February 14th 2020 at 14:15.
Your inspection of the exam will take place in room 4/200 in the Mathematikon on February 19th 2020 at 14:00-15:00.
The lecture is organized into two parts.
Part 1 is devoted to convex analysis and programming which play a key role in computational data analysis and also provide the basis for nonconvex problems (Part 2). Keywords: smooth and nonsmooth convex analysis, conjugation and duality, conic programs, operator splitting, deterministic and stochastic convex optimization.
Part 2 is devoted to nonconvex problems with additional structure that enables to design convergent algorithms. Keywords: elementary Riemannian manifolds, retractions, nonpositive curvature, Riemannian means, Kurdyka-Lojasiewicz property and global proximal optimization.
Basic problems from machine learning and computational data analysis illustrate the application of these concepts.
English or German, as the audience requests.
Students of mathematics and scientific computing interested in numerical optimization, with a focus on applications to data analysis and machine learning.
Mandatory undergraduate courses on analysis and linear algebra.
If you wish to attend the lecture and the exercises, please sign up using MÜSLI.
Each week there will be an exercise sheet you can voluntarily work on. The exercises will not be collected and corrected, but the solutions will be presented in the exercise class.
Some exercise sheets contain (voluntary) programming exercises, which also will be discussed in the exercise class. We recommend programming the exercises with Python and numpy. A basic understanding of Python and numpy should be sufficient for most exercises.
If you cannot attend the exam on February 14th 2020, write a mail to Alexander Zeilmann until February 21th 2020, 23:59 stating that you want to attend a second exam.
The second exam will (most likely) take place around the beginning of the next semester. So far the date is not fixed.
Further information:
Go to the Wolfram Programming Lab and click on the orange button. This brings you to a tutorial notebook. With the file menu in the light grey bar, you can create an empty notebook. In the notebook, you can paste the code from the code files below. Execute the code with Shift+Enter.
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Table of Contents (Jan 6)
Introduction (update: Oct 18)
Literature
Preliminaries: SVD
Smooth Convex Functions
Nonsmooth Convex Functions, Convex Sets, Optimality (update: Nov 25)
Nonexpansive Operators (update: Nov 25)
Convex Optimisation Algorithms 1
Convex Optimisation Algorithms 2
Conjugation, Duality
Nonconvex Optimization (update: Jan 21)
You need to log in to access the exercise sheets.