Summer school on Aspects of Optimization
With three foci: discrete, continuous, and stochastic
The multi-perspective summer school on Aspects of Optimization with three foci: discrete, continuous, and stochastic is scheduled to take place in Klagenfurt on September 12-16, 2022.
Three minicourses on continuous optimization, stochastic optimal control, and discrete optimization aim to give an introduction to the topics for (PhD) students in mathematics with different educational background. Each minicourse is concluded with a research talk by the course instructor. Master students as well as advanced bachelor students are welcome to participate.
This summer school is organized within the scope of the FWF funded doc.funds doctoral school Modeling – Analysis – Optimization of discrete, continuous, and stochastic systems. The doctoral school is part of the newly established area of key research strength Multiple Perspectives in Optimization (MPOpt) at the University of Klagenfurt.
Participation is free of charge, but active participation in the courses and exercises is expected.
| When: | September 12-16, 2022 |
| Where: | AAU Klagenfurt, HS 1, Location map |
| Registration: | Click here to register (until July 31, 2022) |
| Contact: | roswitha [dot] rissner [at] aau [dot] at |
Our speakers:
Claudia d’Ambrosio: Discrete Optimization
Discrete Optimization
Claudia D’Ambrosio
CNRS & École Polytechnique, France
Integer programming (IP) concerns optimization problems where part or all the decision variables have to take integer values. A wide variety of real-world applications falls in this class of optimization problems, thus studying them and the methods aimed at solving them has a strong interest both in theory and practice. IP problems are very challenging due to their intrinsic combinatorial aspect. After some notions of polyhedral theory, we will show when finding integer solutions is possible through efficient methods. Then, we will introduce the concept of relaxations and ideal formulations and comparison among alternative formulations of notable problems. Furthermore, we will cover the theory of valid inequalities and will introduce strong valid inequalities and facets for some classic problems. Finally, we will focus on the most widely used methods for integer programming: branch-and-bound, cutting-planes, branch-and-cut.
Ekaterina Kostina: Continuous Optimization
Continuous Optimization
Ekaterina Kostina
Universität Heidelberg, Germany
Mathematical and computational optimization is a highly topical research area of enormous relevance in all areas of advanced science and engineering that rely on mathematical models and computational simulation. This course is devoted to continuous optimization, one of the sub-areas of mathematical optimization that deals with optimization problems with continuous variables. The aim of the course is to introduce fundamentals of nonlinear optimization theory and methods. We will start with optimality conditions for nonlinear unconstrained and constrained optimization. Then we will continue with basic algorithms for unconstrained optimization including steepest descent, Newton’ method and quasi-Newton methods, and strategies ensuring convergence such as line-search and trust-region methods. We will discuss implementation details and convergence properties of the methods. Finally, we will give an overview of practical optimization algorithms for constrained optimization including Sequential Quadratic Programming (SQP) and interior-point methods.
Ralf Wunderlich: Stochastic optimal control
Stochastic Optimal Control
Ralf Wunderlich
BTU Cottbus–Senftenberg, Germany
The aim of this course is to provide an introduction to continuous-time stochas-
tic optimal control problems and to study an application to dynamic portfolio
optimization. First we will review some underlying tools from stochastic calculus
such as continuous-time stochastic processes, martingales, stochastic integration,
Itˆo’s formula, stochastic differential equations and Dynkin’s formula.
Based on these concepts we will then formulate a general stochastic optimal
control problem which we will solve using the dynamic programming approach.
Finally, we solve a specific portfolio selection problem for an utility maximizing
investor.
Lecture Notes
https://www.math.b-tu.de/INSTITUT/lswima/Courses/SOC22.pdf
Appendix
https://www.math.b-tu.de/INSTITUT/lswima/Courses/SOC22_app.pdf
General Introduction
https://www.math.b-tu.de/INSTITUT/lswima/Courses/SOC22_intro_general.pdf
Research talk
https://www.math.b-tu.de/INSTITUT/lswima/Courses/Klagenfurt2022.pdf
Timetable:
| 09:00 / 09:45 | Welcome Coffee |
| 09:45 / 10:00 | Opening |
| 10:00 / 12:00 | Ralf Wunderlich |
| Lunch | |
| 13:00 / 15:00 | Ralf Wunderlich |
| Time for exercises |
| 08:30 / 10:30 | Claudia d‘Ambrosio |
| Break | |
| 11:00 / 13:00 | Claudia d‘Ambrosio |
| Lunch, Time for exercises | |
| 16:30 / 18:30 | Ralf Wunderlich |
| 08:30 / 10:30 | Ekaterina Kostina |
| Break | |
| 11:00 / 13:00 | Ralf Wunderlich |
| Lunch | |
| 14:30 / 15:00 | Ralf Wunderlich |
| Break | |
| 16:00 / 18:30 | Claudia d‘Ambrosio |
| 08:30 / 10:30 | Claudia d‘Ambrosio |
| Break | |
| 11:00 / 13:00 | Ekaterina Kostina |
| Lunch, Time for exercises |
| 08:30 / 10:30 | Ekaterina Kostina |
| Break | |
| 11:00 / 13:30 | Ekaterina Kostina |
Quicklinks
Information for
Address
Universitätsstraße 65-67
9020 Klagenfurt am Wörthersee
Austria
+43 463 2700
uni [at] aau [dot] at
www.aau.at
Campus Plan
