https://www.dagstuhl.de/09391

# Algorithms and Complexity for Continuous Problems

## Organisatoren

Thomas Müller-Gronbach (Universität Passau, DE)
Leszek Plaskota (University of Warsaw, PL)
Joseph F. Traub (Columbia University – New York, US)

## Off Topic

Art exhibition by Johannes Buchmann opens on Tuesday September 22. All participants are invited to attend after dinner on 7:30 pm.

## Summary

This was already the 10th Dagstuhl Seminar on Algorithms and Complexity for Continuous Problems over a period of 18 years. It brings together researchers from different communities working on computational aspects of continuous problems, including computer scientists, numerical analysts, applied and pure mathematicians, and statisticians. Although the Seminar title has remained the same many of the topics and participants change with each Seminar. Each seminar in this series is of a very interdisciplinary nature.

Continuous problems arise in diverse areas of science and engineering. Examples include multivariate and path integration, approximation, optimization, operator equations, (stochastic) ordinary as well as (stochastic) partial differential equations. Typically, only partial and/or noisy information is available, and the aim is to solve the problem with a given error tolerance using the minimal amount of computational resources. For example, in multivariate numerical integration one wants to compute an $\varepsilon$-approximation to the integral with the minimal number of function evaluations.

Still growing need of efficiently solving more and more complicated computational problems makes this branch of science both important and challenging. The current seminar attracted 58 participants from 11 different countries all over the world. About 30% of them were young researchers including PhD students. There were 53 presentations covering in particular the following topics:

• tractability of high dimensional problems
• computational stochastic processes
• numerical analysis of operator equations
• inverse and ill-posed problems
• applications in computer graphics and finance

The work of the attendants was supported by a variety of funding agencies. This includes the Deutsche Forschungsgemeinschaft, the National Science Foundation and the Defense Advanced Research Projects Agency (USA), and the Australian Research Council. Many of the attendants from Germany were supported within the DFG priority program SPP 1324 on "Extraction of Quantifiable Information from Complex Systems", which is strongly connected to the topics of the seminar.

As always, the excellent working conditions and friendly atmosphere provided by the Dagstuhl team have led to a rich exchange of ideas as well as a number of new collaborations.

Selected papers related to this seminar will be published in a special issue of the Journal of Complexity.

## Classification

• Data Structures / Algorithms / Complexity

## Keywords

• Quantum computation
• Tractability
• High-dimensional problems
• Operator equations
• Computational learning theory
• Computational stochastic processes

## Buchausstellung

Buchausstellung im Erdgeschoss der Bibliothek

(nur in der Veranstaltungswoche).

## Dokumentation

In der Reihe Dagstuhl Reports werden alle Dagstuhl-Seminare und Dagstuhl-Perspektiven-Workshops dokumentiert. Die Organisatoren stellen zusammen mit dem Collector des Seminars einen Bericht zusammen, der die Beiträge der Autoren zusammenfasst und um eine Zusammenfassung ergänzt.