CIMPA-ICTP Math Courses 2022 - From Monday 5 December to Thursday 8 December at 14:00 (Gebrie)/hybrid seminar

[ICTP Math Section]

CIMPA/ICTP MATH COURSES  2022

Hybrid Course on:

Introduction to Optimization and Operator Theory


This is a recurring zoom meeting, therefore please register just once 
for all 4 sessions:
https://zoom.us/meeting/register/tJUodOihqDMvE9fOe6s-MziaNCKeZeoaVSDt



Timetable and venue (for those attending in person):

Monday 5 December:   14:00 - 16:00 - Stasi Seminar Room
Tuesday 6 December:  14:00 - 16:00 - Stasi Seminar Room
Wednesday 7 December: 14:00 - 16:00 - Stasi Seminar Room
Thursday 8 December: 14:00 - 16:00 - Stasi Seminar Room




Title: Introduction to Optimization and Operator Theory


Speaker: GEBRIE Anteneh Getachew (Debre Berhan University)


Abstract: An introductory lecture on operator and optimization theory 
will be given. To be specific, various notions of derivatives for 
mappings between Normed spaces will be discussed, with a special 
emphasis on mappings taking values in R connecting derivatives with 
optimization problems. We discuss the continuity, lower semicontinuity, 
differentiability, and, most importantly, optimization properties of 
convex functions in normed spaces. We will also go over the Fenchel 
conjugate and biconjugate for convex functions, as well as their 
properties. With these tools at our disposal, we move on to the duality 
methods in optimization, which allows us to solve unconstrained and 
constrained minimization problems (called the primal) by relating them 
to their dual problems obtained via the Fenchel conjugate. Finally, 
after discussing the Moreau proximity operator in Hilbert spaces, we 
will look at a popular class of optimization algorithms.

References:
[1] Kravvaritis, D. C., & Yannacopoulos, A. N. (2020). Variational 
methods in nonlinear analysis: with applications in optimization and 
partial differential equations. Walter De Gruyter Gmbh & Co Kg.
[2] Bauschke, H. H., & Combettes, P. L. (2011). Convex analysis and 
monotone operator theory in Hilbert spaces (Vol. 408). New York: Springer.



Please note: The CIMPA/ICTP Courses will be recorded and broadcasted.



https://indico.ictp.it/event/10141/