Convex Analysis (AN11): Διαφορά μεταξύ των αναθεωρήσεων
Χωρίς σύνοψη επεξεργασίας |
Χωρίς σύνοψη επεξεργασίας |
||
Γραμμή 1: | Γραμμή 1: | ||
* [[Κυρτή Ανάλυση (AN11)|Ελληνική Έκδοση]] | * [[Κυρτή Ανάλυση (AN11)|Ελληνική Έκδοση]] | ||
{{Course-Graduate-Top-EN}} | {{Course-Graduate-Top-EN}} | ||
{{Menu-OnAllPages-EN}} | |||
=== General === | === General === |
Τελευταία αναθεώρηση της 16:26, 15 Ιουνίου 2023
- Ελληνική Έκδοση
- Graduate Courses Outlines
- Outline Modification (available only for faculty members)
- Department of Mathematics
- Save as PDF or Print (to save as PDF, pick the corresponding option from the list of printers, located in the window which will popup)
General
School | School of Science |
---|---|
Academic Unit | Department of Mathematics |
Level of Studies | Graduate |
Course Code | AN11 |
Semester | 2 |
Course Title | Convex Analysis |
Independent Teaching Activities | Lectures (Weekly Teaching Hours: 3, Credits: 7.5) |
Course Type | Specialized general knowledge |
Prerequisite Courses |
Real Analysis, Calculus I and Calculus II |
Language of Instruction and Examinations |
Greek |
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 graduate level. Material varies from classical topics on convex analysis to recent research problems. The students should:
|
---|---|
General Competences |
|
Syllabus
Basic notions. Convex functions and convex sets, convexity criteria. Normed spaces. Dual spaces and the Legendre transform. The Caratheodory Theorem and its applications to geometry. Radon’s and Helly’s theorems. Minkowski’s First theorem and its applications to Optimization Theory. The concentration of measure phenomenon on the sphere. Dvoretzky’s theorem and the Quotient of Subspace theorem. The Brunn-Minkowski inequality and its generalizations (Lp variants and functional forms). Mixed volumes and inequalities of Aleksandrov-Fenchel type. Inequalities of isoperimetric type (e.g. the classical isoperimetric inequality and the Blaschke-Santalo inequality). The Brascamp-Lieb inequality and reverse isoperimetric inequalities. Area measures of convex hypersurfaces. The Minkowski Existence and Uniqueness problem and its generalizations, applications to the Theory of Monge-Ampere equations. Classical open problems.
Teaching and Learning Methods - Evaluation
Delivery |
Lectures/ Class presentations | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology | - | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
Students choose evaluation by one or both of the following:
In case that a student participates to both, the final grade is the maximum of the two grades. 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
- J. Bakelman, Convex Analysis And Nonlinear Geometric Elliptic Equations
- R. J. Gardner, Geometric tomography. Second edition.
- H. Groemer, Geometric Applications of Fourier Series and Spherical Harmonics.
- Koldobsky, Fourier Analysis in Convex Geometry.
- M. Ledoux, The Concentration of Measure Phenomenon.
- V.D. Milman and G. Schechtman, Asymptotic Theory of Finite Dimensional Normed Spaces
- R. Tyrel Rockafellar, Convex Analysis.
- R. Schneider, Convex bodies: the Brunn-Minkowski theory. Second expanded edition.
- R. Schneider and W. Weil, Stochastic and Integral Geometry.
- C. Thompson, Minkowski Geometry.