Numerical Methods and Optimization An Introduction Chapman & Hall/CRC Numerical Analysis and Scientific Computing Series

For students in industrial and systems engineering (ISE) and operations research (OR) to understand optimization at an advanced level, they must first grasp the analysis of algorithms, computational complexity, and other concepts and modern developments in numerical methods. Satisfying this prerequisite, Numerical Methods and Optimization: An Introduction combines the materials from introductory numerical methods and introductory optimization courses into a single text. This classroom-tested approach enriches a standard numerical methods syllabus with optional chapters on numerical optimization and provides a valuable numerical methods background for students taking an introductory OR or optimization course.

The first part of the text introduces the necessary mathematical background, the digital representation of numbers, and different types of errors associated with numerical methods. The second part explains how to solve typical problems using numerical methods. Focusing on optimization methods, the final part presents basic theory and algorithms for linear and nonlinear optimization.

The book assumes minimal prior knowledge of the topics. Taking a rigorous yet accessible approach to the material, it includes some mathematical proofs as samples of rigorous analysis but in most cases, uses only examples to illustrate the concepts. While the authors provide a MATLAB® guide and code available for download, the book can be used with other software packages.

Basics: Preliminaries. Numbers and Errors. Numerical Methods for Standard Problems: Elements of Numerical Linear Algebra. Solving Equations. Polynomial Interpolation. Numerical Integration. Numerical Solution of Differential Equations. Introduction to Optimization: Basic Concepts. Complexity Issues. Introduction to Linear Programming. The Simplex Method for Linear Programming. Duality and Sensitivity Analysis in Linear Programming. Unconstrained Optimization. Constrained Optimization. Notes and References. Bibliography. Index.