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From 20.09.15 to 25.09.15, the Dagstuhl Seminar 15391 Algorithms and Complexity for Continuous Problems was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, participants presented their current research, and ongoing work and open problems were discussed. Abstracts or the presentations given during the seminar can be found in this report. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available.

From 23.09.12 to 28.09.12, the Dagstuhl Seminar 12391 Algorithms and Complexity for Continuous Problems was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar can be found in this report. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available.

From 20.09.09 to 25.09.09, the Dagstuhl Seminar 09391 Algorithms and Complexity for Continuous Problems was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available.

From 26.09.04 to 01.10.04, the Dagstuhl Seminar ``Algorithms and Complexity for Continuous Problems'' was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available.

The goal of this workshop was to bring together researchers from different communities working on computational aspects of continuous problems. Continuous computational problems arise in many areas of science and engineering. Examples include path and multivariate integration, function approximation, optimization, as well as differential, integral, and operator equations. Understanding the complexity of such problems and constructing efficient algorithms is both important and challenging. The workshop was of a very interdisciplinary nature with invitees from, e.g., computer science, numerical analysis, discrete, applied, and pure mathematics, physics, statistics, and scientific computation. Many of the lectures were presented by Ph.D. students. Compared to earlier meetings, several very active research areas received more emphasis. These include Quantum Computing, Complexity and Tractability of high-dimensional problems, Stochastic Computation, and Quantization, which was an entirely new field for this workshop. Due to strong connections between the topics treated at this workshop many of the participants initiated new cooperations and research projects. For more details, see the pdf-file with the same title.

This is an article that will appear in the Encyclopedia of Optimization (Kluwer, 2000). It concerns optimization in two senses. The first is that information-based complexity (IBC) is the study of the minimal computational resources to solve continuous mathematical problems. The second is that the computational complexity of optimization problems is one of the areas studied in IBC. We discuss IBC and information-based optimization in turn.

Should the impossibility results of theoretical computer science be of concern to physics?

I’ll discuss the unknown and the unknowable in science, raising more questions than I will answer. I will also talk about two topics which have been much in the news in 1996, and which might erroneously be confused with my topic.

This article lies at the intersection of computational physics and theoretical computer science. Over the last 60 years there has been a stream of negative results announcing undecidability, non-computability, and intractability. Are these impossibility results relevant to physics? I will discuss two of the negative results and provide arguments regarding their relevance.

Monte Carlo simulation is widely used to price complex financial instruments Recent theoretical results and extensive computer testing indicate that deterministic methods may be far superior in speed and confidence. Simulations using the Sobol or Faure points are examples of deterministic methods. For the sake of brevity we refer to a deterministic method using the name of the sequence of points which the method uses (e.g. Sobol method.)

"I’ll discuss the six critical areas from May 1986. When I speak about them from my 1996 vantage, I’m giving only my own view; I’ve not had the benefit of discussing these opinions with the Board. Our number one concern in May 1986 was Competitiveness. How can the U.S. best ensure the continued leadership of its computer science and technology enterprise in the face of intensified global competition?"

A paper that claims that "The mathematical model is an abstraction of the natural world while the model of computation is an abstraction of the computer world."