Convex Analysis (MAE753)

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School of Science

Academic Unit

Department of Mathematics

Level of Studies


Course Code




Course Title

Convex Analysis

Independent Teaching Activities

Lectures (Weekly Teaching Hours: 3, Credits: 6)

Course Type

Special Background

Prerequisite Courses -
Language of Instruction and Examinations


Is the Course Offered to Erasmus Students

Yes (in English)

Course Website (URL) See eCourse, the Learning Management System maintained by the University of Ioannina.

Learning Outcomes

Learning outcomes

The course aims to an introduction to convex analysis at undergraduate level. It is desired for students to understand convex sets with respect to some of their qualitative (from a geometric/combinatorial point of view) and quantitative (e.g. volume, surface area) properties together with the study of the corresponding convex functions.

General Competences
  • Working independently
  • Team work
  • Production of free, creative and inductive thinking
  • Production of analytic and synthetic thinking
  • Search for, analysis and synthesis of data and information, with the use of the necessary technology
  • Get in touch with specialized knowledge and evolve abilities for comparing, obtaining and evaluating results on the specific area of interest.


Basic notions. Convex functions and convex sets. Polytopes. Gauge functions and support functions. The Caratheodory. Radon's and Helly's theorems. Minkowski's First theorem. The Brunn-Minkowski inequality. Mixed volumes. Inequalities of isoperimetric type (e.g. the classical isoperimetric inequality and the Blaschke-Santalo inequality). F. John's Theorem. The reverse isoperimetric inequality.

Teaching and Learning Methods - Evaluation


Lectures/ Class presentations

Use of Information and Communications Technology Use of the platform “E-course” of the University of Ioannina
Teaching Methods
Activity Semester Workload
Lectures/Presentations 39
Assignments/Essays 33
Individual study 78
Course total 150
Student Performance Evaluation

Students' evaluation by the following:

  • Class presentation - Essays - Assignments
  • Final Written Examination

Evaluation criteria and all steps of the evaluation procedure will be accessible to students through the platform "E-course" of the University of Ioannina.

Attached Bibliography

See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:

  • R. J. Gardner, Geometric tomography. Second edition. Cambridge University Press, 2006.
  • R. Tyrel Rockafellar, Convex Analysis. Princeton University Press, 1970.
  • R. Schneider, Convex bodies: the Brunn-Minkowski theory. Second expanded edition. Cambridge University Press, 2014.
  • A. C. Thompson, Minkowski Geometry. Cambridge University Press, 1996.
  • R. Webster, Convexity. Oxford University Press, 1970.