Algorithms for Minimization Without Derivatives (Dover Books on Mathematics)

Book Details

• Publisher: Dover

• Author: Richard P. Brent

• Language: English

• ISBN: 9780486419985

• Pages: 208

• Cover: Paperback

• Release Date: 20-03-2013

• Dimensions: 8.4 x 5.4 x 0.7 inches

• Format: Illustrated

About The Book

Algorithms for Minimization without Derivatives by Richard P. Brent is an essential text for graduate students and researchers interested in optimization and numerical analysis. The book explores the process of finding local and global minima for functions without the need for derivative evaluation. This is particularly important in practical scenarios where derivatives are difficult or impossible to compute, a common challenge in many scientific and engineering problems.

Brent's work provides significant improvements to existing algorithms, extending their mathematical theories and offering new, practical algorithms for approximating minima. The book covers a range of topics including:

• Successive interpolation for finding simple zeros of a function and its derivatives.

• An algorithm with guaranteed convergence for minimizing a function of one variable.

• Global minimization techniques given an upper bound on the second derivative.

• A new algorithm for minimizing functions of several variables without the need for derivatives.

In addition to the theoretical discussion, the book is supported by numerous numerical examples. It includes a complete analysis of the rate of convergence for most algorithms, as well as error bounds that account for rounding errors, making it an invaluable resource for those involved in computational mathematics.

Key Features:

• No Derivatives Required: All algorithms are based on sequential function evaluation, eliminating the need for derivative calculations.

• Practical Algorithms: Designed for scenarios where derivatives are difficult to evaluate, making the book highly practical for real-world applications.

• Convergence Analysis: Provides a thorough analysis of the rate of convergence and error bounds, critical for understanding the performance of the algorithms.

• Numerical Examples: The text includes numerous examples to illustrate the algorithms and their applications.

This book is an indispensable resource for anyone working in optimization, numerical methods, or computational science, particularly when dealing with functions where derivatives are not readily available.