A First Course in Optimization

Description

Features Explains how to find exact and approximate solutions to systems of linear equations Shows how to use linear programming techniques, iterative methods, and specialized algorithms in various applications Discusses the importance of speeding up convergence Presents the necessary mathematical tools and results to provide the proper foundation Prepares readers to understand how iterative optimization methods are used in inverse problems Includes exercises at the end of each chapter Solutions manual available upon qualifying course adoption Give Your Students the Proper Groundwork for Future Studies in Optimization A First Course in Optimization is designed for a one-semester course in optimization taken by advanced undergraduate and beginning graduate students in the mathematical sciences and engineering. It teaches students the basics of continuous optimization and helps them better understand the mathematics from previous courses. The book focuses on general problems and the underlying theory. It introduces all the necessary mathematical tools and results. The text covers the fundamental problems of constrained and unconstrained optimization as well as linear and convex programming. It also presents basic iterative solution algorithms (such as gradient methods and the Newton–Raphson algorithm and its variants) and more general iterative optimization methods. This text builds the foundation to understand continuous optimization. It prepares students to study advanced topics found in the author’s companion book, Iterative Optimization in Inverse Problems, including sequential unconstrained iterative optimization methods.