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Recent Advances in Nonsmooth Optimization
Nonsmooth optimization covers the minimization or maximization of functions which do not have the differentiability properties required by classical methods. The field of nonsmooth optimization is significant, not only because of the existence of nondifferentiable functions arising directly in applications, but also because several important methods for solving difficult smooth problems lead directly to the need to solve nonsmooth problems, which are either smaller in dimension or simpler in structure. This book contains twenty five papers written by forty six authors from twenty countries in five continents. It includes papers on theory, algorithms and applications for problems with first-o...
Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan
This book is a tribute to Professor Ian Hugh Sloan on the occasion of his 80th birthday. It consists of nearly 60 articles written by international leaders in a diverse range of areas in contemporary computational mathematics. These papers highlight the impact and many achievements of Professor Sloan in his distinguished academic career. The book also presents state of the art knowledge in many computational fields such as quasi-Monte Carlo and Monte Carlo methods for multivariate integration, multi-level methods, finite element methods, uncertainty quantification, spherical designs and integration on the sphere, approximation and interpolation of multivariate functions, oscillatory integral...
Proceedings of the 2009 Joint Workshop of Fraunhofer IOSB and Institute for Anthropomatics, Vision and Fusion Laboratory
The joint workshop of the Fraunhofer Institute of Optronics, System Technologies and Image Exploitation IOSB, Karlsruhe, and the Vision and Fusion Laboratory (Institute for Anthropomatics, Karlsruhe Institute of Technology (KIT)), is organized annually since 2005 with the aim to report on the latest research and development findings of the doctoral students of both institutions. This book provides a collection of 16 technical reports on the research results presented on the 2009 workshop.
Recent Progress in Multivariate Approximation
Nineteen contributions cover recent topics in constructive approximation on varieties, approximation by solutions of partial differential equations, application of Riesz bases and frames, multiwavelets and subdivision. An essential resource for researchers and graduates in applied mathematics, computer science and geophysics who are interested in the state-of-the-art developments in multivariate approximation.
Recent Advances in Nonsmooth Optimization
Nonsmooth optimization covers the minimization or maximization of functions which do not have the differentiability properties required by classical methods. The field of nonsmooth optimization is significant, not only because of the existence of nondifferentiable functions arising directly in applications, but also because several important methods for solving difficult smooth problems lead directly to the need to solve nonsmooth problems, which are either smaller in dimension or simpler in structure.This book contains twenty five papers written by forty six authors from twenty countries in five continents. It includes papers on theory, algorithms and applications for problems with first-order nondifferentiability (the usual sense of nonsmooth optimization) second-order nondifferentiability, nonsmooth equations, nonsmooth variational inequalities and other problems related to nonsmooth optimization.
An Invitation to Geomathematics
The authors introduce geomathematics as an active research area to a wider audience. Chapter 1 presents an introduction to the Earth as a system to apply scientific methods. Emphasis is laid on transfers from virtual models to reality and vice versa. In the second chapter geomathematics is introduced as a new scientific area which nevertheless has its roots in antiquity. The modern conception of geomathematics is outlined from different points of view and its challenging nature is described as well as its interdisciplinarity. Geomathematics is shown as the bridge between the real world and the virtual world. The complex mathematical tools are shown from a variety of fields necessary to tackl...
Probabilistic Models of Cosmic Backgrounds
Combining research methods from various areas of mathematics and physics, Probabilistic Models of Cosmic Backgrounds describes the isotropic random sections of certain fiber bundles and their applications to creating rigorous mathematical models of both discovered and hypothetical cosmic backgrounds. Previously scattered and hard-to-find mathematical and physical theories have been assembled from numerous textbooks, monographs, and research papers, and explained from different or even unexpected points of view. This consists of both classical and newly discovered results necessary for understanding a sophisticated problem of modelling cosmic backgrounds. The book contains a comprehensive des...
Handbook of Geomathematics
During the last three decades geosciences and geo-engineering were influenced by two essential scenarios: First, the technological progress has changed completely the observational and measurement techniques. Modern high speed computers and satellite based techniques are entering more and more all geodisciplines. Second, there is a growing public concern about the future of our planet, its climate, its environment, and about an expected shortage of natural resources. Obviously, both aspects, viz. efficient strategies of protection against threats of a changing Earth and the exceptional situation of getting terrestrial, airborne as well as spaceborne data of better and better quality explain ...
Scientific and Engineering Computations for the 21st Century - Methodologies and Applications
The 20th century saw tremendous achievements and progress in science and technology. Undoubtedly, computers and computer-related technologies acted as one of vital catalysts for accelerating this progress in the latter half of the century. The contributions of mathematical sciences have been equally profound, and the synergy between mathematics and computer science has played a key role in accelerating the progress of both fields as well as science and engineering. Mathematical sciences will undoubtedly continue to play this vital role in this new century. In particular, mathematical modeling and numerical simulation will continue to be among the essential methodologies for solving massive a...
Reformulation: Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods
The concept of "reformulation" has long been playing an important role in mathematical programming. A classical example is the penalization technique in constrained optimization that transforms the constraints into the objective function via a penalty function thereby reformulating a constrained problem as an equivalent or approximately equivalent unconstrained problem. More recent trends consist of the reformulation of various mathematical programming prob lems, including variational inequalities and complementarity problems, into equivalent systems of possibly nonsmooth, piecewise smooth or semismooth nonlinear equations, or equivalent unconstrained optimization problems that are usually d...
