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.
A log-quadratic projection method for convex feasibility problems (A. Auslender, M. Teboulle).
Projection algorithms: Results and open problems (H.H. Bauschke).
Joint and separate convexity of the bregman distance (H.H. Bauschke, J.M. Borwein).
A parallel algorithm for non-cooperative resource allocation games (L.M. Bregman, I.N. Fokin).
Asymptotic behavior of quasi-nonexpansive mappings (D. Butnariu, S. Reich, A.J. Zaslavski).
The outer bregman projection method for stochastic feasibility
problems in banach spaces (D. Butnariu, E. Resmerita).
Bregman-legendre multidistance projection algorithms for convex
feasibility and optimization (C. Byrne).
Averaging strings of sequential iterations for convex feasibility
problems (Y. Censor, T. Elfving, G.T. Herman).
Quasi-fejerian analysis of some optimization algorithms (P.L. Combettes).
On the theory and practice of row relaxation methods (A. Dax).
From parallel to sequential projection methods and vice versa in convex feasibility: Results and conjectures (A.R. De Pierro).
Accelerating the convergence of the method of alternating projections via line search: A brief survey (F. Deutsch).
PICO: An object-oriented framework for parallel branch and bound
(J. Eckstein, C.A. Phillips, W.E. Hart).
Approaching equilibrium in parallel (S.D. Flam).
Generic convergence of algorithms for solving stochastic feasibility problems (M. Gabour, S. Reich, A.J. Zaslavski).
Superlinear rate of convergence and optimal acceleration schemes in the solution of convex inequality problems (M. Garcia-Palomares).
Algebraic reconstruction techniques using smooth basis functions for helical cone-beam tomography (G.T. Herman, S. Matej, B.M. Carvalho).
Compact operators as products of projections (H.S. Hundal).
Parallel subgradient methods for convex optimization (K.C. Kiwiel, P.O. Lindberg).
Directional halley and quasi-halley methods in
N variables (Y. Levin, A. Ben-Israel).
Ergodic convergence to a zero of the extended sum of two
maximal monotone operators (A. Moudafi, M. Thera).
Distributed asynchronous incremental subgradient methods (A. Nedic, D.P. Bertsekas, V.S. Borkar).
Random algorithms for solving convex inequalities (B.T. Polyak).
Parallel iterative methods for sparse linear systems (Y. Saad).
On the relation between bundle methods for maximal monotone
inclusions and hybrid proximal point algorithms (C.A. Sagastizabal, M.V. Solodov).
New optimized and accelerated PAM methods for solving large
non-symmetric linear systems: Theory and practice (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 (I. Yamada).