Algorithms and Complexity for Continuous Problems

Continuous computational problems arise in diverse areas of science and engineering. There has been an increasing interest in computational aspects of multivariate problems. Examples include path and multivariate integration, function approximation, optimization, and operator equations. Understanding the complexity of such problems and construction of efficient algorithms is both important and challenging.

The main focus of this seminar will be on the complexity of such high dimensional problems and on their tractability. Efficient or, ideally, optimal algorithms will be presented. Since Monte Carloand/or quasi-Monte Carlo algorithms are often used for such problems, their efficiency will also be addressed. Models of computations and various settings (e.g., worst case, average case, or probabilistic) are important part of the complexity study and these will be discussed as well.