Fixed-Point Algorithms for Inverse Problems in Science and Engineering [electronic resource] /
Bauschke, Heinz H.editor.
Burachik, Regina S.editor.
Combettes, Patrick L.editor.
Elser, Veit.editor.
Luke, D. Russell.editor.
Wolkowicz, Henry.editor.
  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.
Description based upon print version of record.
Fixed-Point Algorithms forInverse Problems in Scienceand Engineering; Preface; Contents; Contributors; Chapter 1 Chebyshev Sets, Klee Sets, and Chebyshev Centerswith Respect to Bregman Distances: Recent Resultsand Open Problems; 1.1 Introduction; 1.1.1 Legendre Functions and Bregman Distances; 1.1.2 Nearest Distance, Nearest Points, and Chebyshev Sets; 1.1.3 Farthest Distance, Farthest Points, and Klee Sets; 1.1.4 Chebyshev Radius and Chebyshev Center; 1.1.5 Goal of the Paper; 1.1.6 Organization of the Paper; 1.2 Auxiliary Results; 1.3 Chebyshev Sets; 1.4 Klee Sets
1.5 Chebyshev Centers: Uniqueness and Characterization1.6 Chebyshev Centers: Two Examples; 1.6.1 Diagonal-Symmetric Line Segments in the Strictly Positive Orthant; 1.6.2 Intervals of Real Numbers; 1.7 Generalizations and Variants; 1.8 List of Open Problems; 1.9 Conclusion; References; Chapter 2 Self-Dual Smooth Approximations of Convex Functions via the Proximal Average; 2.1 Introduction; 2.2 The Goebel Smoothing Operator; 2.3 A New Smoothing Operator; References; Chapter 3 A Linearly Convergent Algorithm for Solving a Classof Nonconvex/Affine Feasibility Problems; 3.1 Introduction
3.2 Problem Statement, Motivation and Examples3.2.1 General Problem Statement; 3.2.2 Motivation and Examples; 3.3 A Scalable Restricted Isometry Property (SRIP); 3.3.1 Convex Relaxation and Restricted Isometry; 3.3.1.1 The Good News; 3.3.1.2 The Bad News; 3.3.2 Scalable Restricted Isometry Property; 3.4 A Linearly Convergent Gradient Projection Method; 3.4.1 The Gradient Projection Method for Solving Problem (NCF); 3.4.2 Linear Rate of Convergence Analysis for GP; References; Chapter 4 The Newton Bracketing Method for Convex Minimization: Convergence Analysis; 4.1 Introduction
4.2 Bracket Reduction in the NB Method for n=14.3 Bracket Reduction in the NB Method for n>1; 4.4 Application to the Fermat-Weber Location Problem; References; Chapter 5 Entropic Regularization of the lo Function; 5.1 Introduction; 5.1.1 Elementary bold0mu mumu 1 Minimization; 5.1.2  lo Minimization; 5.1.3 Notation; 5.2 Entropic Regularization of the Zero Metric; 5.3 Algorithms: Subgradient Descent; 5.3.1 Nonsmooth Case: bold0mu mumu =0; 5.3.2 Dynamically Rescaled Descent with Exact Line Search; 5.4 Convergence to Sparse Solutions; 5.5 Greedy Algorithms; 5.6 Numerical Examples
5.6.1 Our ``Toy'' Problem5.6.2 Algorithm Illustrations; 5.6.3 Complexity; 5.7 Comments and Conclusion; References; Chapter 6 The Douglas-Rachford Algorithm in the Absenceof Convexity; 6.1 Introduction; 6.2 Preliminaries; 6.3 Local Convergence When 0  7.3 Fenchel Duality
Includes bibliographical references.
  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.
Computer mathematics.
Calculus of variations.
Mathematical models.
Algorithms.
Mathematical physics.
Computational Mathematics and Numerical Analysis.
Calculus of Variations and Optimal Control; Optimization.
Mathematical Modeling and Industrial Mathematics.
Algorithm Analysis and Problem Complexity.
Theoretical, Mathematical and Computational Physics.
Springer optimization and its applications