Linear and Nonlinear Programming (4th Edition)

October 31, 2020
Linear and Nonlinear Programming (4th Edition)

This new edition covers the central concepts of practicaloptimization techniques, with an emphasis on methods that are bothstate-of-the-art and popular. One major insight is the connectionbetween the purely analytical character of an optimization problemand the behavior of algorithms used to solve a problem. This was amajor theme of the first edition of this book and the fourthedition expands and further illustrates this relationship. As inthe earlier editions, the material in this fourth edition isorganized into three separate parts. Part I is a self-containedintroduction to linear programming. The presentation in this partis fairly conventional, covering the main elements of theunderlying theory of linear programming, many of the most effectivenumerical algorithms, and many of its important specialapplications. Part II, which is independent of Part I, covers thetheory of unconstrained optimization, including both derivations ofthe appropriate optimality conditions and an introduction to basicalgorithms. This part of the book explores the general propertiesof algorithms and defines various notions of convergence. Part IIIextends the concepts developed in the second part to constrainedoptimization problems. Except for a few isolated sections, thispart is also independent of Part I. It is possible to go directlyinto Parts II and III omitting Part I, and, in fact, the book hasbeen used in this way in many universities.New to this edition is a chapter devoted to Conic LinearProgramming, a powerful generalization of Linear Programming.Indeed, many conic structures are possible and useful in a varietyof applications. It must be recognized, however, that conic linearprogramming is an advanced topic, requiring special study. Anotherimportant topic is an accelerated steepest descent method thatexhibits superior convergence properties, and for this reason, hasbecome quite popular. The proof of the convergence property forboth standard and accelerated steepest descent methods arepresented in Chapter 8. As in previous editions, end-of-chapterexercises appear for all chapters.