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Linear and Nonlinear Optimization

Igor Griva, Stephen G. Nash, and Ariela Sofer
Publication Date: 
Number of Pages: 
[Reviewed by
Brian Borchers
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This book is the second edition of a textbook on linear and nonlinear programming that was originally published by McGraw Hill in 1996. The overall outline of the second edition is similar to the first edition. The first edition was marred by many typographical errors that have been corrected in the second edition. Furthermore, the new edition has been expanded to include additional topics including filter methods, nonlinear primal-dual methods, and semidefinite programming.

The book consists of four parts, beginning with a section that introduces optimization and gives several examples, a section on the simplex method and interior point methods for linear programming, a section on methods for unconstrained nonlinear optimization, and a section on methods for constrained nonlinear optimization. Background material from linear algebra, vector calculus, and analysis appears in appendices.

There are many other textbooks for first courses in optimization at the graduate level. The topical coverage of this textbook is fairly similar to the coverage in Luenberger and Ye (2008) and Nocedal and Wright (2006.) In comparison with those textbooks, the strength of this book is in its intuitive explanations of the concepts behind the various algorithms and its extensive examples. Furthermore, the material in this book is presented at a somewhat lower mathematical level that should make it more accessible to students with limited mathematical background. However the theoretical development in Nocedal and Wright is more thorough.

This textbook might be suitable for a two semester graduate course on linear and nonlinear programming. For students who already have had a course in linear programming, the book could also be used for a one semester course on nonlinear programming.


David G. Luenberger and Yinyu Ye. Linear and Nonlinear Programming, Third Edition. Springer, 2008.

J. Nocedal and S. Wright. Numerical Optimization, 2nd edition. Springer, 2006.

Brian Borchers is a professor of Mathematics at the New Mexico Institute of Mining and Technology. His interests are in optimization and applications of optimization in parameter estimation and inverse problems.