Bavarian AI Chair for Mathematical Foundations of Artificial Intelligence
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Convex Optimization

Course Description

Optimization is a fundamental tool for data science and machine learning. From a practical point of view, it is crucial to understand the convergence behavior of the various optimization methods. In light of modern large-scale applications, resource efficient first-order methods are here of particular interest. Relying on the mathematical theory of convex analysis, it is possible to derive rigorous convergence rates for such methods. Moreover, the developed theory often can be transferred to general non-convex problems.
This lecture will provide an introduction into the basic concepts of convex analysis and will show, how the theory can be used to analyze the convergence behavior of first-order methods like gradient descent. In particular, the presented methods will be linked to concrete data science problems. The topics we discuss will encompass:

  • Convex Analysis
  • First-order methods like gradient descent, proximal gradient descent, mirror descent, etc.
  • Second-order methods like Newton’s method and quasi-Newton methods

Prerequisites

The course is targeted at Master students from mathematics. Basic knowledge of functional analysis is highly recommended.

Schedule and Venue

Lecture (by Prof. Dr. Johannes Maly): Tue 10-12 and Thu 10-12 in room B 251

Exercise class (by Mariia Seleznova): Di 14-16 in room B 134 and Mi 10-12 in room B 046. Please note that only one of the exercises per week is mandatory as they cover the same content. You may choose the one that best fits your schedule.

Office Hour (Johannes Maly): Tue 13-14 in Akademiestr. 7, floor 5, room 515. Please email me the day before office hours to let me know if you plan to attend.

Office Hour (Mariia Seleznova): Tue 12-13 in Akademiestr. 7, floor 5, room 511. Please email me the day before office hours to let me know if you plan to attend.

Creditable Modules

WP35 Fortgeschrittene Themen aus der künstlichen Intelligenz
Data Science (9 ECTS)

WP 26 Fortgeschrittene Themen aus der numerischen Mathematik

Other modules in MSc Mathematik and MSc Finanz- und Versicherungsmathematik are possible as well. Interested students shall directly approach the Prüfungsamt and inform us.

Registration

Register at moodle https://moodle.lmu.de/course/view.php?id=33102 (enrollment key is cods).