The Mathematics of Nonlinear Programming [Paperback]

Nonlinear programming provides an excellent opportunity to explore an interesting variety of pure and solidly applicable mathematics, numerical analysis, and computing. This text develops some of the ideas and techniques involved in the optimization methods using calculus, leading to the study of convexity. This is followed by material on basic numerical methods, least squares, the Karush-Kuhn-Tucker theorem, penalty functions, and Lagrange multipliers. The authors have aimed their presentation at the student who has a working knowledge of matrix algebra and advanced calculus, but has had no previous exposure to optimization.This book is designed for a first course in nonlinear optimization. It starts with classical optimization notions from calculus and proceeds smoothly to a study of convex functions. This is followed by material on basic numerical methods, least squares, Karush-Kuhn-Tucker theory, penalty functions, and Lagrange multipliers. The book has been tested in the classroom; the approach is rigorous at all times and geometric intuition is developed. The numerical methods are up-to-date. The presentation emphasizes the mathematical ideas behind computer codes.The book is aimed at the student who has a working knowledge of linear algebra and partial differentiation but has had no previous exposure to optimization. Mathematics instructors will be comfortable with the mathematical approach which deemphasizes recipes and emphasizes understanding underlying concepts. There are many exercises chosen to highlight the fundamental ideas.Preface; 1: Unconstrained Optimization via Calculus; 2: Convex and Convex Functions; 3: Iterative Methods for Unconstrained Optimization; 4: Least Squares Optimization; 5: Convex Programming and the Karush-Kuhn-Tucker Conditions; 6: Penalty Methods; 7: Optimization with Equality Constraints; IndexThe book is aimed at students who have a working knowledge of linear algebra and partial differentiation but has had no previous exposurel3Ä