β Scribed by Heinz H. Bauschke, Mason S. Macklem (auth.), Heinz H. Bauschke, Regina S. Burachik, Patrick L. Combettes, Veit Elser, D. Russell Luke, Henry Wolkowicz (eds.)
No coin nor oath required. For personal study only.
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 βInterdisciplinary Workshop on Fixed-Point Algorithms for Inverse Problems in Science and Engineeringβ 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:
Β· 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
Β· 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
Β· 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.
Front Matter....Pages i-xi
Chebyshev Sets, Klee Sets, and Chebyshev Centers with Respect to Bregman Distances: Recent Results and Open Problems....Pages 1-21
Self-Dual Smooth Approximations of Convex Functions via the Proximal Average....Pages 23-32
A Linearly Convergent Algorithm for Solving a Class of Nonconvex/Affine Feasibility Problems....Pages 33-48
The Newton Bracketing Method for Convex Minimization: Convergence Analysis....Pages 49-64
Entropic Regularization of the β 0 Function....Pages 65-92
The DouglasβRachford Algorithm in the Absence of Convexity....Pages 93-109
A Comparison of Some Recent Regularity Conditions for Fenchel Duality....Pages 111-130
Non-Local Functionals for Imaging....Pages 131-154
Opial-Type Theorems and the Common Fixed Point Problem....Pages 155-183
Proximal Splitting Methods in Signal Processing....Pages 185-212
Arbitrarily Slow Convergence of Sequences of Linear Operators: A Survey....Pages 213-242
Graph-Matrix Calculus for Computational Convex Analysis....Pages 243-259
Identifying Active Manifolds in Regularization Problems....Pages 261-271
Approximation Methods for Nonexpansive Type Mappings in Hadamard Manifolds....Pages 273-299
Existence and Approximation of Fixed Points of Bregman Firmly Nonexpansive Mappings in Reflexive Banach Spaces....Pages 301-316
Regularization Procedures for Monotone Operators: Recent Advances....Pages 317-344
Minimizing the Moreau Envelope of Nonsmooth Convex Functions over the Fixed Point Set of Certain Quasi-Nonexpansive Mappings....Pages 345-390
The BrΓ©zis-Browder Theorem Revisited and Properties of Fitzpatrick Functions of Order n ....Pages 391-402
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 Computa
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