E-Book Overview
Fixed-Point Algorithms for Inverse Problems in Science and Engineering presents some of the most recent work from leading researchers in variational and numerical analysis. The contributions in this collection provide state-of-the-art theory and practice in first-order fixed-point algorithms, identify emerging problems driven by applications, and discuss new approaches for solving these problems.
This book is a compendium of topics explored at the Banff International Research Station “Interdisciplinary Workshop on Fixed-Point Algorithms for Inverse Problems in Science and Engineering” in November of 2009. The workshop included a broad range of research including variational analysis, numerical linear algebra, biotechnology, materials science, computational solid-state physics, and chemistry.
Key topics and features of this book include:
· Theory of Fixed-point algorithms: variational analysis, convex analysis, convex and nonconvex optimization, subdifferential calculus, nonsmooth analysis, proximal point methods, projection methods, resolvent and related fixed-point theoretic methods, and monotone operator theory
· Numerical analysis of fixed-point algorithms: choice of step lengths, of weights, of blocks for block-iterative and parallel methods, and of relaxation parameters; regularization of ill-posed problems; numerical comparison of various methods
· Applications: Image and signal processing, antenna optimization, location problems
The wide scope of applications presented in this volume easily serve as a basis for new and innovative research and collaboration.
E-Book Content
Fixed-Point Algorithms for Inverse Problems in Science and Engineering For further volumes: http://www.springer.com/series/7393 Springer Optimization and Its Applications VOLUME 49 Managing Editor Panos M. Pardalos (University of Florida) Editor–Combinatorial Optimization Ding-Zhu Du (University of Texas at Dallas) Advisory Board J. Birge (University of Chicago) C.A. Floudas (Princeton University) F. Giannessi (University of Pisa) H.D. Sherali (Virginia Polytechnic and State University) T. Terlaky (McMaster University) Y. Ye (Stanford University) Aims and Scope Optimization has been expanding in all directions at an astonishing rate during the last few decades. New algorithmic and theoretical techniques have been developed, the diffusion into other disciplines has proceeded at a rapid pace, and our knowledge of all aspects of the field has grown even more profound. At the same time, one of the most striking trends in optimization is the constantly increasing emphasis on the interdisciplinary nature of the field. Optimization has been a basic tool in all areas of applied mathematics, engineering, medicine, economics and other sciences. The series Springer Optimization and Its Applications publishes undergraduate and graduate textbooks, monographs and state-of-the-art expository works that focus on algorithms for solving optimization problems and also study applications involving such problems. Some of the topics covered include nonlinear optimization (convex and nonconvex), network flow problems, stochastic optimization, optimal control, discrete optimization, multi-objective programming, description of software packages, approximation techniques and heuristic approaches. Heinz H. Bauschke • Regina S. Burachik Patrick L. Combettes • Veit Elser D. Russell Luke • Henry Wolkowicz Editors Fixed-Point Algorithms for Inverse Problems in Science and Engineering ABC Editors Heinz H. Bauschke Department of Mathematics and Statistics University of British Columbia Okanagan Campus Kelowna, British Columbia Canada
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