Nonlinear optimization: complexity issues
Nonlinear optimization: complexity issues
Methods and Applications of Interval Analysis (SIAM Studies in Applied and Numerical Mathematics) (Siam Studies in Applied Mathematics, 2.)
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This chapter contains selected papers presented at the Minisymposium on Interval Methods of the PARA'04 Workshop “State-of-the-Art in Scientific Computing”. The emphasis of the workshop was on high-performance computing (HPC). The ongoing development of ever more advanced computers provides the potential for solving increasingly difficult computational problems. However, given the complexity of modern computer architectures, the task of realizing this potential needs careful attention. A main concern of HPC is the development of software that optimizes the performance of a given computer. An important characteristic of the computer performance in scientific computing is the accuracy of the computation results. Often, we can estimate this accuracy by using traditional statistical techniques. However, in many practical situations, we do not know the probability distributions of different measurement, estimation, and/or roundoff errors, we only know estimates of the upper bounds on the corresponding measurement errors, i.e., we only know an interval of possible values of each such error. The papers from the following chapter contain the description of the corresponding “interval computation” techniques, and the applications of these techniques to various problems of scientific computing.