Parallel Optimization Theory, Algorithms, and Applications [Hardcover]

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.

Foreword,George B. Dantzig
Preface
Acknowledgments
Glossary of Symbols
1. Introduction
PART I. THEORY
2. Generalized Distances and Generalized Projections
3. Proximal Minimization withD-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

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, thougl<