Nonlinear Programming: Theory and Algorithms / Edition 3

Hardcover (Print)
Buy New
Buy New from
Used and New from Other Sellers
Used and New from Other Sellers
from $96.35
Usually ships in 1-2 business days
(Save 39%)
Other sellers (Hardcover)
  • All (9) from $96.35   
  • New (5) from $122.89   
  • Used (4) from $96.35   



Nonlinear Programming: Theory and Algorithms—now in an extensively updated Third Edition—addresses the problem of optimizing an objective function in the presence of equality and inequality constraints. Many realistic problems cannot be adequately represented as a linear program owing to the nature of the nonlinearity of the objective function and/or the nonlinearity of any constraints. The Third Edition begins with a general introduction to nonlinear programming with illustrative examples and guidelines for model construction.

Concentration on the three major parts of nonlinear programming is provided:

  • Convex analysis with discussion of topological properties of convex sets, separation and support of convex sets, polyhedral sets, extreme points and extreme directions of polyhedral sets, and linear programming
  • Optimality conditions and duality with coverage of the nature, interpretation, and value of the classical Fritz John (FJ) and the Karush-Kuhn-Tucker (KKT) optimality conditions; the interrelationships between various proposed constraint qualifications; and Lagrangian duality and saddle point optimality conditions
  • Algorithms and their convergence, with a presentation of algorithms for solving both unconstrained and constrained nonlinear programming problems

Important features of the Third Edition include:

  • New topics such as second interior point methods, nonconvex optimization, nondifferentiable optimization, and more
  • Updated discussion and new applications in each chapter
  • Detailed numerical examples and graphical illustrations
  • Essential coverage of modeling and formulating nonlinear programs
  • Simple numerical problems
  • Advanced theoretical exercises

The book is a solid reference for professionals as well as a useful text for students in the fields of operations research, management science, industrial engineering, applied mathematics, and also in engineering disciplines that deal with analytical optimization techniques. The logical and self-contained format uniquely covers nonlinear programming techniques with a great depth of information and an abundance of valuable examples and illustrations that showcase the most current advances in nonlinear problems.

Read More Show Less

Editorial Reviews

From the Publisher
"The promotional message on the back cover proclaims 'this book is a solid reference for professionals and a useful text for students…"; and I fully agree." (Technometrics, February 2007)

"Noted and recommended for its logical format and sharp editing that never wavers in its focus." (Electric Review, September/October 2006)

"…highly recommended for a course in the theory of nonlinear programming…" (MAA Reviews, July 17, 2006)

 ‘… ‘the Bazaraa’ is a must if you are interested in optimization…’ (Journal of the Operational Research Society, 2007)

A self-contained text/reference dealing with convex analysis, optimality conditions and duality, and computational methods--presented with numerical examples, graphical illustrations, and exercises. Useful as a reference for topics in nonlinear programming and as a text in the fields of operations research, management science, industrial engineering, and applied math, and in engineering disciplines that deal with analytical optimization techniques. Requires some mathematical maturity and a working knowledge of linear algebra and calculus. Annotation c. Book News, Inc., Portland, OR (
Read More Show Less

Product Details

  • ISBN-13: 9780471486008
  • Publisher: Wiley
  • Publication date: 5/5/2006
  • Edition description: REV
  • Edition number: 3
  • Pages: 872
  • Sales rank: 579,390
  • Product dimensions: 6.38 (w) x 9.25 (h) x 1.98 (d)

Meet the Author

Mokhtar S. BAZARAA, PhD, is a Professor at the Georgia Institute of Technology.

HANIF D. SHERALI, PhD, is a W. Thomas Rice Chaired Professor of Engineering in the Grado Department of Industrial and Systems Engineering at Virginia Polytechnic Institute and State University.

C. M. SHETTY, PhD, is a Professor Emeritus at the Georgia Institute of Technology.
Professors Bazaraa and Sherali are also coauthors of the complementary bestselling book, Linear Programming and Network Flows, Third Edition, also published by Wiley.

Read More Show Less

Table of Contents

Chapter 1 Introduction.

1.1 Problem Statement and Basic Definitions.

1.2 Illustrative Examples.

1.3 Guidelines for Model Construction.


Notes and References.

Part 1 Convex Analysis.

Chapter 2 Convex Sets.

2.1 Convex Hulls.

2.2 Closure and Interior of a Set.

2.3 Weierstrass's Theorem.

2.4 Separation and Support of Sets.

2.5 Convex Cones and Polarity.

2.6 Polyhedral Sets, Extreme Points, and Extreme Directions.

2.7 Linear Programming and the Simplex Method.


Notes and References.

Chapter 3 Convex Functions and Generalizations.

3.1 Definitions and Basic Properties.

3.2 Subgradients of Convex Functions.

3.3 Differentiable Convex Functions.

3.4 Minima and Maxima of Convex Functions.

3.5 Generalizations of Convex Functions.


Notes and References.

Part 2 Optimality Conditions and Duality.

Chapter 4 The Fritz John and Karush-Kuhn-Tucker Optimality Conditions.

4.1 Unconstrained Problems.

4.2 Problems Having Inequality Constraints.

4.3 Problems Having Inequality and Equality Constraints.

4.4 Second-Order Necessary and Sufficient Optimality Conditions for Constrained Problems.


Notes and References.

Chapter 5 Constraint Qualifications.

5.1 Cone of Tangents.

5.2 Other Constraint Qualifications.

5.3 Problems Having Inequality and Equality Constraints.


Notes and References.

Chapter 6 Lagrangian Duality and Saddle Point Optimality Conditions.

6.1 Lagrangian Dual Problem.

6.2 Duality Theorems and Saddle Point Optimality Conditions.

6.3 Properties of the Dual Function.

6.4 Formulating and Solving the Dual Problem

6.5 Getting the Primal Solution.

6.6 Linear and Quadratic Programs.


Notes and References.

Part 3 Algorithms and Their Convergence.

Chapter 7 The Concept of an Algorithm.

7.1 Algorithms and Algorithmic Maps.

7.2 Closed Maps and Convergence.

7.3 Composition of Mappings.

7.4 Comparison Among Algorithms.


Notes and References.

Chapter 8 Unconstrained Optimization.

8.1 Line Search Without Using Derivatives.

8.2 Line Search Using Derivatives.

8.3 Some Practical Line Search Methods.

8.4 Closedness of the Line Search Algorithmic Map.

8.5 Multidimensional Search Without Using Derivatives.

8.6 Multidimensional Search Using Derivatives.

8.7 Modification of Newton's Method: Levenberg-Marquardt and Trust Region Methods.

8.8 Methods Using Conjugate Directions: Quasi-Newton and Conjugate Gradient Methods.

8.9 Subgradient Optimization Methods.


Notes and References.

Chapter 9 Penalty and Barrier Functions.

9.1 Concept of Penalty Functions.

9.2 Exterior Penalty Function Methods.

9.3 Exact Absolute Value and Augmented Lagrangian Penalty Methods.

9.4 Barrier Function Methods.

9.5 Polynomial-Time Interior Point Algorithms for Linear Programming Based on a Barrier Function.


Notes and References.

Chapter 10 Methods of Feasible Directions.

10.1 Method of Zoutendijk.

10.2 Convergence Analysis of the Method of Zoutendijk.

10.3 Successive Linear Programming Approach.

10.4 Successive Quadratic Programming or Projected Lagrangian Approach.

10.5 Gradient Projection Method of Rosen.

10.6 Reduced Gradient Method of Wolfe and Generalized Reduced Gradient Method.

10.7 Convex-Simplex Method of Zangwill.

10.8 Effective First- and Second-Order Variants of the Reduced Gradient Method.


Notes and References.

Chapter 11 Linear Complementary Problem, and Quadratic, Separable, Fractional, and Geometric Programming.

11.1 Linear Complementary Problem.

11.2 Convex and Nonconvex Quadratic Programming: Global Optimization Approaches.

11.3 Separable Programming.

11.4 Linear Fractional Programming.

11.5 Geometric Programming.


Notes and References.

Appendix A Mathematical Review.

Appendix B Summary of Convexity, Optimality Conditions, and Duality.



Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star


4 Star


3 Star


2 Star


1 Star


Your Rating:

Your Name: Create a Pen Name or

Barnes & Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation


  • - By submitting a review, you grant to Barnes & and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Terms of Use.
  • - Barnes & reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)