-1. Chebyshev Sets, Klee Sets, and Chebyshev Centers with respect to Bregman Distances: Recent Results and Open Problems (H. Bauschke, M. Macklem, S.X. Wang). -2. Self-dual Smooth Approximations of Convex Functions via the Proximal Average (H. Bauschke, S. Moffat, S.X. Wang). -3. A Linearly Convergent Algorithm for Solving a Class of Nonconvex/Affine Feasibility Problems (A. Beck, M. Teboulle). -4. The Newton Bracketing Method for Convex Minimization: Convergence Analysis (A. Ben-Israel, Y. Levin). -5. Entropic regularization of the ℓ0 function (J. Borwein, D. Luke). -6. The Douglas-Rachford algorithm in the absence of convexity (J. Borwein, B. Sims). -7. A comparison of some recent regularity conditions for Fenchel duality (R. Boţ, E. Czetnek). -8. Non-Local Functionals for Imaging (J. Boulanger, P. Elbau, C. Pontow, O. Scherzer). -9. Opial-Type Theorems and the Common Fixed Point Problem (A. Cegielski, Y. Censor). -10. Proximal Splitting Methods in Signal Processing (P. Combettes, J. Pesquet). -11. Arbitrarily Slow Convergence of Sequences of Linear Operators: A Survey (F. Deutsch, H. Hundal). -12. Graph-Matrix Calculus for Computational Convex Analysis (B. Gardiner, Y. Lucet). -13. Identifying Active Manifolds in Regularization Problems (W. Hare). -14. Approximation methods for nonexpansive type mappings in Hadamard manifolds (G. López, V. Martín-Márquez). -15. Existence and Approximation of Fixed Points of Bregman Firmly Nonexpansive Mappings in Reflexive Banach Spaces (S. Reich, S. Sabach). -16. Regularization procedure for monotone operators: recent advances (J. Revalski). -17. Minimizing the Moreau Envelope of Nonsmooth Convex Functions over the Fixed Point Set of Certain Quasi-Nonexpansive Mappings (I. Yamada, M. Yukawa, M. Yamagishi). -18. The Brézis-Browder Theorem revisted and properties of Fitzpatrick functions of order n (L. Yao).
<p> </p><p><i>Fixed-Point Algorithms for Inverse Problems in Science and Engineering</i> 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.</p><p> </p><p>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.</p><p> </p><p>Key topics and features of this book include:</p><p>· 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</p><p>· 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</p><p>· Applications: Image and signal processing, antenna optimization, location problems</p><p> </p><p>The wide scope of applications presented in this volume easily serve as a basis for new and innovative research and collaboration. </p><p></p>
