Parallel Optimization: Theory, Algorithms and Applications(Numerical Mathematics and Scientific Computation)

This book offers a unique pathway to methods of parallel optimization by introducing parallel computing ideas and techniques into both optimization theory, and into some numerical algorithms for large-scale optimization problems. The presentation is based on the recent understanding that rigorous mathematical analysis of algorithms, parallel computing techniques, and "hands-on" experimental work on real-world problems must go hand in hand in order to achieve the greatest advantage from novel parallel computing architectures. The three parts of the book thus bring together relevant theory, careful study of algorithms, and modelling of significant real world problems. The problem domains include: image reconstruction, radiation therapy treatment planning, transportation problems, portfolilo management, and matrix estimation. This text can be used both as a reference for researchers and as a text for advanced graduate courses.

Table of Contents:
George B. Dantzig: Foreword Preface Acknowledgments Glossary of Symbols 1: Introduction PART I. THEORY 2: Generalized Distances and Generalized Projections 3: Proximal Minimization with D-Functions 4: Penalty Methods, Barrier Methods and Augmented Lagrangians PART II. ALGORITHMS 5: Iterative Methods for Convex Feasibility Problems 6: Iterative Algorithms for Linearly Constrained Optimization Problems 7: Model Decomposition Algorithms 8: Decompositions in Interior Point Algorithms PART III. APPLICATIONS 9: Matrix Estimation Problems 10: Image Reconstruction from Projections 11: The Inverse Problem in Radiation Therapy Treatment Planning 12: Multicommodity Network Flow Problems 13: Planning Under Uncertainty 14: Decompositions for Parallel Computing 15: Numerical Investigations

Review :
"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 "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