Rigorous Global Search: Continuous Problems

Rigorous Global Search: Continuous Problems

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This work grew out of several years of research, graduate seminars and talks on the subject. It was motivated by a desire to make the technology accessible to those who most needed it or could most use it. It is meant to be a self-contained introduction, a reference for the techniques, and a guide to the literature for the underlying theory. It contains pointers to fertile areas for future research. It also serves as introductory documentation for a Fortran 90 software package for nonlinear systems and global optimization. The subject of the monograph is deterministic, automatically verified or r- orous methods. In such methods, directed rounding and computational fix- point theory are combined with exhaustive search (branch and bound) te- niques. Completion of such an algorithm with a list of solutions constitutes a rigorous mathematical proof that all of the solutions within the original search region are within the output list. The monograph is appropriate as an introduction to research and technology in the area, as a desk reference, or as a graduate-level course reference. Kno- edge of calculus, linear algebra, and elementary numerical analysis is assumed.
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Product details

  • Hardback | 264 pages
  • 149.9 x 231.1 x 30.5mm | 430.92g
  • Dordrecht, Netherlands
  • English
  • 1996 ed.
  • XVI, 264 p.
  • 0792342380
  • 9780792342380

Back cover copy

The book provides a self-contained introduction to underlying techniques, as well as a compendium of theory and a guide to the author's Fortran 90 software for nonlinear algebraic systems and global, constrained optimization with automatic result verification. Besides introductory and survey material, the book contains unique research results. The book also contains non-traditional ideas concerning non-smooth optimization. Thus, the book should be a valuable reference to applied mathematicians and computational scientists and engineers. With numerous examples and exercises, as well as leads for future research, the book can be used as a graduate text or reference on interval arithmetic, automatic differentiation and interval fixed point theory. The book can also serve as a user's guide for the nonlinear equations and optimization software, available free of charge from the author, for the author's general Fortran 90 interval arithmetic package, or for the associated automatic differentiation package. Audience: Researchers in operations research, numerical analysis, computational chemistry, computer-aided geometric design and computational geometry, robot kinematics, remote sensing. Also suitable for graduate and topics courses in numerical analysis, optimization, and operations research.
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Table of contents

List of Figures. List of Tables. Preface. 1. Preliminaries. 2. Software Environments. 3. On Preconditioning. 4. Verified Solution of Nonlinear Systems. 5. Optimization. 6. Non-Differentiable Problems. 7. Use of Intermediate Quantities in the Expression Values. References. Index.
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