Parallel Optimization: Theory, Algorithms, and Applications

by Yair Censor, Stavros A. Zenios

Overview

This book offers a unique pathway to methods of parallel optimization by introducing parallel computing ideas into both optimization theory and into some numerical algorithms for large-scale optimization problems. The three parts of the book bring together relevant theory, careful study of algorithms, and modeling of significant real world problems such as image reconstruction, radiation therapy treatment planning, financial planning, transportation and multi-commodity network flow problems, planning under uncertainty, and matrix balancing problems.

Product Details

ISBN-13:	9780195100624
Publisher:	Oxford University Press
Publication date:	01/08/1998
Series:	Numerical Mathematics and Scientific Computation
Pages:	576
Product dimensions:	9.20(w) x 6.20(h) x 1.20(d)

About the Author

University of Haifa

University of Cyprus

Table of Contents

Foreword, George B. DantzigPrefaceAcknowledgmentsGlossary of Symbols1. IntroductionPART I. THEORY2. Generalized Distances and Generalized Projections3. Proximal Minimization with D-Functions4. Penalty Methods, Barrier Methods and Augmented LagrangiansPART II. ALGORITHMS5. Iterative Methods for Convex Feasibility Problems6. Iterative Algorithms for Linearly Constrained Optimization Problems7. Model Decomposition Algorithms8. Decompositions in Interior Point AlgorithmsPART III. APPLICATIONS9. Matrix Estimation Problems10. Image Reconstruction from Projections11. The Inverse Problem in Radiation Therapy Treatment Planning12. Multicommodity Network Flow Problems13. Planning Under Uncertainty14. Decompositions for Parallel Computing15. Numerical Investigations

Editorial Reviews

"This book presents a domain that arises where two different branches of science, namely parallel computations and the theory of constrained optimization, intersect with real life problems. This domain, called parallel optimization, has been developing rapidly under the stimulus of progress in computer technology. The book focuses on parallel optimization methods for large-scale constrained optimization problems and structured linear problems. . . . [It] covers a vast portion of parallel optimization, though full coverage of this domain, as the authors admit, goes far beyond the capacity of a single monograph. This book, however, in over 500 pages brings an excellent and in-depth presentation of all the major aspects of a process which matches theory and methods of optimization with modern computers. The volume can be recommended for graduate students, faculty, and researchers in any of those fields."—Mathematical Reviews

From the Publisher