The 1st Alps-Adriatic Inverse Problems Summer School will be held at the Department of Mathematics of the Alpen-Adria-Universitaet Klagenfurt during July 3-4, 2023.
The aim of this Summer School is to provide scientists at an early stage of the career (PhD students, postdocs) with an introduction to some topical areas in inverse problems.
Participants might also take the opportunity to attend the subsequent 3rd Alps-Adriatic Inverse Problems Workshop (July 5-7, 2023).
The summer school will be held in person.
Radu Ioan Boţ (University of Vienna)
Title: Numerical methods for convex and nonconvex optimization
Abstract: The aim of the lecture series is to present an overview of numerical methods for solving convex and nonconvex optimization problems, with possible smooth and/or nonsmooth additive terms in the objective function.
The first three lectures will be devoted to the convex setting and will address basic numerical methods, the role of the splitting paradigm when solving composite optimization problems, convergence rate estimates, and techniques to accelerate the convergence of some of the numerical algorithms. Special attention will be payed to the interplay between continuous time and discrete time methods.
In the fourth lecture we will review some of the iterative schemes with provable convergence properties for nonconvex optimization problems with structures which range from simple to complex. We will discuss the main aspects of the convergence analysis and also emphasize the role played by the Kurdyka- Lojasiewicz property in proving global convergence.
The theoretical considerations will be illustrated by various numerical experiments.
William Rundell (Texas A&M University):
Title: Inverse Problems for Fractional Partial Differential Equations
Abstract: The use of anomalous diffusion processes to model physical phenomena began some 50 years ago. From a mathematical perspective this brought in the use of fractional derivatives as key components of the resulting differential equations. Over the last decade there has been enormous interest in the study of inverse problems involving these fractional equations. One of the interesting questions is whether the inverse problem under fractional operators is more or less ill-posed than its classical counterpart. In the latter case there is the intriguing question whether the fractional model can be used as an effective regularising term for the case of integer order derivatives.
This series of talks will attempt to explore the above questions using a variety of models and differential equations of the three main types.
Registration: May 17, 2023
Local Organizing Committee:
- Phuoc Truong Huynh
- Barbara Kaltenbacher
- Teresa Rauscher
- Elena Resmerita
- Anita Wachter
- Tobias Wolf
- Barbara Kaltenbacher, Klagenfurt
- Elena Resmerita, Klagenfurt
All talks take place at room HS 4 (quite near the main entrance of the University) and the breaks in room Z.1.08 (right next to HS 4)
The 1st Alps-Adriatic Inverse Problems Summer School 2023 is supported by the doc.funds doctoral school: