Parallel optimization : theory, algorithms, and applications

書誌事項

Parallel optimization : theory, algorithms, and applications

Yair Censor, Stavros A. Zenios

(Numerical mathematics and scientific computation)

Oxford University Press, 1997

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注記

Includes bibliographical references (p. 481-526) and index

内容説明・目次

内容説明

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.

目次

  • Foreword
  • Preface
  • Glossary of Symbols
  • 1. Introduction
  • Part I Theory
  • 2. Generalized Distances and Generalized Projections
  • 3. Proximal Minimization with D-Functions
  • Part II Algorithms
  • 4. Penalty Methods, Barrier Methods and Augmented Lagrangians
  • 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 Reconsturction 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

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