Dan Butnariu, Yair Censor and Simeon Reich (Eds.)9780444505958, 0444505954
Inherently parallel algorithms, that is, computational methods which are, by their mathematical nature, parallel, have been studied in various contexts for more than fifty years. However, it was only during the last decade that they have mostly proved their practical usefulness because new generations of computers made their implementation possible in order to solve complex feasibility and optimization problems involving huge amounts of data via parallel processing. These led to an accumulation of computational experience and theoretical information and opened new and challenging questions concerning the behavior of inherently parallel algorithms for feasibility and optimization, their convergence in new environments and in circumstances in which they were not considered before their stability and reliability. Several research groups all over the world focused on these questions and it was the general feeling among scientists involved in this effort that the time has come to survey the latest progress and convey a perspective for further development and concerted scientific investigations. Thus, the editors of this volume, with the support of the Israeli Academy for Sciences and Humanities, took the initiative of organizing a Workshop intended to bring together the leading scientists in the field. The current volume is the Proceedings of the Workshop representing the discussions, debates and communications that took place. Having all that information collected in a single book will provide mathematicians and engineers interested in the theoretical and practical aspects of the inherently parallel algorithms for feasibility and optimization with a tool for determining when, where and which algorithms in this class are fit for solving specific problems, how reliable they are, how they behave and how efficient they were in previous applications. Such a tool will allow software creators to choose ways of better implementing these methods by learning from existing experience.
Table of contents :
Content:
Preface
Pages vii-viii
Dan Butnariu, Yair Censor, Simeon Reich
A log-quadratic projection method for convex feasibility problems Original Research Article
Pages 1-9
A. Auslender, Marc Teboulle
Projection algorithms: Results and open problems Original Research Article
Pages 11-22
Heinz H. Bauschke
Joint and separate convexity of the bregman distance Original Research Article
Pages 23-36
Heinz H. Bauschke, Jonathan M. Borwein
A parallel algorithm for non-cooperative resource allocation games Original Research Article
Pages 37-48
L.M. Bregman, I.N. Fokin
Asymptotic behavior of quasi-nonexpansive mappings Original Research Article
Pages 49-68
Dan Butnariu, Simeon Reich, Alexander J. Zaslavski
The outer bregman projection method for stochastic feasibility problems in banach spaces Original Research Article
Pages 69-86
Dan Butnariu, Elena Resmerita
Bregman-legendre multidistance projection algorithms for convex feasibility and optimization Original Research Article
Pages 87-99
Charles Byrne
Averaging strings of sequential iterations for convex feasibility problems Original Research Article
Pages 101-113
Y. Censor, T. Elfving, G.T. Herman
Quasi-Fejérian analysis of some optimization algorithms Original Research Article
Pages 115-152
Patrick L. Combettes
On theory and practice of row relaxation methods Original Research Article
Pages 153-186
Achiya Dax
From parallel to sequential projection methods and vice versa in convex feasibility: Results and conjectures Original Research Article
Pages 187-201
Alvaro R. De Pierro
Accelerating the convergence of the method of alternating projections via a line search: A brief survey Original Research Article
Pages 203-217
F. Deutsch
Pico: An object-oriented framework for parallel branch and bound Original Research Article
Pages 219-265
Jonathan Eckstein, Cynthia A. Phillips, William E. Hart
Approaching equilibrium in parallel Original Research Article
Pages 267-278
Sjur Didrik Flåm
Generic convergence of algorithms for solving stochastic feasibility problems Original Research Article
Pages 279-295
Manal Gabour, Simeon Reich, Alexander J. Zaslavski
Superlinear rate of convergence and optimal acceleration schemes in the solution of convex inequality problems Original Research Article
Pages 297-305
Ubaldo M. García-Palomares
Algebraic reconstruction techniques using smooth basis functions for helical cone-beam tomography Original Research Article
Pages 307-324
G.T. Herman, S. Matej, B.M. Carvalho
Compact operators as products of projections Original Research Article
Pages 325-334
Hein S. Hundal
Parallel subgradient methods for convex optimization Original Research Article
Pages 335-344
K.C. Kiweil, P.O. Lindberg
Directional halley and quasi-halley methods in N variables Original Research Article
Pages 345-367
Yuri Levin, Adi Ben-Israel
Ergodic convergence to a zero of the extended sum of two maximal monotone operators Original Research Article
Pages 369-379
Abdellatif Moudafi, Michel Théra
Distributed asynchronous incremental subgradient methods Original Research Article
Pages 381-407
A. Nedić, D.P. Bertsekas, V.S. Borkar
Random algorithms for solving convex inequalities Original Research Article
Pages 409-422
B.T. Polyak
Parallel iterative methods for sparse linear systems Original Research Article
Pages 423-440
Y. Saad
On the relation between bundle methods for maximal monotone inclusions and hybrid proximal point algorithms Original Research Article
Pages 441-455
Claudia A. Sagastizábal, Mikhail V. Solodov
New optimized and accelerated pam methods for solving large non-symmetric linear systems: Theory and practice Original Research Article
Pages 457-471
H. Scolnik, N. Echebest, M.T. Guardarucci, M.C. Vacchino
The hybrid steepest descent method for the variational inequality problem over the intersection of fixed point sets of nonexpansive mappings Original Research Article
Pages 473-504
Isao Yamada
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