Welcome to the homepage of the lecture Convex Analysis for Visual Computing Winter Term 2007/2008 |
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Lectures (2h) with exercises (2h); 6 ECTS points
Convexity of sets and functions is the central notion in many applications, especially in optimisation and for variational problems. In this lecture, fundamental concepts related to convexity will be explained, for example duality, sublinearity, support-function or subgradient. We always consider finite-dimensional spaces to allow for a certain simplicity and be able to cover practically relevant problems. The usefulness of those notions will be explained with example problems in visual computing. Entrance requirements – Contents – Lecture Notes – Exercises – Assessments / Exams – References
Undergraduate knowledge of mathematics. For computer science students,
this requirement is met by having completed the
The course is concerned with fundamental notions of convex analysis which can be helpful for the understanding of some applications in visual computing. Topics include: - Convex sets and their properties
- Duality, sublinearity, support-function
- Subgradient, set-valued functions and inclusion equations
Here, you can find the hand-written notes after each lecture:
There is also a LaTeXed script written by Kai Hagenburg which can be found here (includes lecture 1 - 9).
The written exam takes place on Thursday, February 28, 2008,
9 - 12 a.m., in lecture hall 003, building E1 3.
- T. Rockafellar, Convex Analysis, Princeton University Press, 1997
- J.-B. Hiriart-Urruty and C. Lemarechal, Convex Analysis and Minimization Algorithms. Part 1: Fundamentals, Second edition, Springer, Berlin, 1996.
- M. J. Panik, Fundamentals of Convex Analysis. Kluwer, 1993.
References related to image processing include research articles and will be given in the lecture. You can find a number of books introducing the topics of the lecture in the reserved reading of the computer science library. |
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