Marc Teboulle – författare

This book provides a systematic and comprehensive account of asymptotic sets and functions from which a broad and useful theory emerges in the areas of optimization and variational inequalities. Mainly it is concerned with the existence of solutions of a given problem in these classes, whenever for example standard compacity hypothesis is not present. Thus it addresses the central problem of handling unbounded situations. This book will be useful to advanced graduate students, researchers, and practitioners in the fields of optimization theory, nonlinear programming, and applied mathematical sciences.

Nonlinear applied analysis and in particular the related ?elds of continuous optimization and variational inequality problems have gone through major developments over the last three decades and have reached maturity. A pivotal role in these developments has been played by convex analysis, a rich area covering a broad range of problems in mathematical sciences and its applications. Separation of convex sets and the Legendre–Fenchel conjugate transforms are fundamental notions that have laid the ground for these fruitful developments. Two other fundamental notions that have contributed to making convex analysis a powerful analytical tool and that haveoftenbeenhiddeninthesedevelopmentsarethenotionsofasymptotic sets and functions. The purpose of this book is to provide a systematic and comprehensive account of asymptotic sets and functions, from which a broad and u- ful theory emerges in the areas of optimization and variational inequa- ties. There is a variety of motivations that led mathematicians to study questions revolving around attaintment of the in?mum in a minimization problem and its stability, duality and minmax theorems, convexi?cation of sets and functions, and maximal monotone maps. In all these topics we are faced with the central problem of handling unbounded situations.

Clustering is one of the most fundamental and essential data analysis techniques. Clustering can be used as an independent data mining task to discern intrinsic characteristics of data, or as a preprocessing step with the clustering results then used for classification, correlation analysis, or anomaly detection.Kogan and his co-editors have put together recent advances in clustering large and high-dimension data. Their volume addresses new topics and methods which are central to modern data analysis, with particular emphasis on linear algebra tools, opimization methods and statistical techniques. The contributions, written by leading researchers from both academia and industry, cover theoretical basics as well as application and evaluation of algorithms, and thus provide an excellent state-of-the-art overview.The level of detail, the breadth of coverage, and the comprehensive bibliography make this book a perfect fit for researchers and graduate students in data mining and in many other important related application areas.