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Trust Region Methods

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A. R. Conn, N. I. M. Gould, and Ph. L. Toint, Editors


2000 / xx + 959 pages / Hardcover / ISBN: 978-0-898714-60-9 / List Price $168.50 / MOS/SIAM Member Price $117.95 / Order Code MP01

This is the first comprehensive reference on trust-region methods, a class of numerical algorithms for the solution of nonlinear convex optimization methods. Its unified treatment covers both unconstrained and constrained problems and reviews a large part of the specialized literature on the subject. It also provides an up-to-date view of numerical optimization.

Written primarily for postgraduates and researchers, the book features an extensive commented bibliography, which contains more than 1000 references by over 750 authors. The book also contains several practical comments and an entire chapter devoted to software and implementation issues. Its many illustrations, including nearly 100 figures, balance the formal and intuitive treatment of the presented topics.

Preface; Chapter 1: Introduction; PART I: PRELIMINARIES. Chapter 2: Basic Concepts; Chapter 3: Basic Analysis and Optimality Conditions; Chapter 4: Basic Linear Algebra; Chapter 5 Krylov Subspace Methods; PART II: TRUST-REGION METHODS FOR UNCONSTRAINED OPTIMIZATION. Chapter 6: Global Convergence of the Basic Algorithm; Chapter 7: The Trust-Region Subproblem; Chapter 8: Further Convergence Theory Issues; Chapter 9: Conditional Models; Chapter 10: Algorithmic Extensions; Chapter 11: Nonsmooth Problems; PART III: TRUST-REGION METHODS FOR CONSTRAINED OPTIMIZATION WITH CONVEX CONSTRAINTS. Chapter 12: Projection Methods for Convex Constraints; Chapter 13: Barrier Methods for Inequality Constraints; PART IV: TRUST-REGION METHODS FOR GENERAL CONSTRAINED OPTIMIZATION AND SYSTEMS OF NONLINEAR EQUATIONS. Chapter 14: Penalty-Function Methods; Chapter 15: Sequential Quadratic Programming Methods; Chapter 16: Nonlinear Equations and Nonlinear Fitting; PART V: FINAL CONSIDERATIONS. Chapter 17: Practicalities; Afterword; Appendix: A Summary of Assumptions; Annotated Bibliography; Subject and Notation Index; Author Index

ISBN: 9780898714609

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