Customer Reviews

Nonlinear Programming: Theory and Algorithms

5 star:		(4)
4 star:		(0)
3 star:		(0)
2 star:		(0)
1 star:		(0)

 

 

I am referring to the Bazaraa, Sherali and Shetty book "Nonlinear Programming, Theory and Applications", second edition (it seems that Amazon missed the third author).

This is a great book for anyone who is interested in nonlinear optimization. The book presents the topic in a clear and concise manner, provides learning aides in form of examples and generally has a very well structured layout. I have other books on NLP, but I consider this the best one (Luenberger is great, too - but very condensed). The book consists of three parts: the first part presents convex analysis, the second part looks at optimality conditions and the third part presents algorithms. If you went through some OR textbooks and felt that they didn't give you enough on NLP, this is the place to get your fix!

This book for NLPs together with Dantzig's work on LPs and you have the basic toolset for static optimization.

I am also referring to the 2nd Edition of the book.

I largely agree with review by Marc Sachon except the part about Dantzig's book: if you are new to LP/NLP, or Mathematical Programming in general, stay away from Dantzig's book. Its writing style is entirely outdated and will put you to sleep in no time. Reading from Dantzig to learn about LP is like reading Newton's originals to learn physics/calculus.

If you're new to LP / NLP I *strongly* recommend Vanderbei, and THEN this book.

This book covers enough ground for fast paced novices and beyond novices.
It's mathematical but not rigorous in the strict mathematician's way - for that kind of exposure look elsewhere. It covers a breadth of subjects/issues related to LP / NLP not often found in other books at its level, so in a way it is like a small compendium.

It's more up-to-date than say, R. Fletcher's "Practical Methods of Optimization", or Gill, Murray & Wright's "Practical Optimization" both good MSc level books but somewhat dated now and perhaps a bit tedious sometimes. However, if you're a novice, I advise you to look at them also, if you have access to them, as they might serve your specific needs/ reading style better/equally well. You should also look at Luenberger's "Linear and Nonlinear Programming" which is also quite old but has a classic writing style and is holding up rather well. If you want the fine nitty-gritty details and the breadth of coverage though, Bazaraa has more. Luenberger's more solid and rigorous.

Haven't had the chance to look at the more recent "Nonlinear Optimization" by Andrzej Ruszczynski but it might be as good/better as he's also an expert in the field - so keep that in mind.

"Convex Optimization" by Stephen Boyd is more advanced (not too advanced though, depending on your maths ability) and moving in a slightly different field/teritory.

This book presents the theory and algorithms of nonlinear programming.

Summaring the contents:

Ch1. Introduction

Part1 Convex Analysis
Ch2. Convex Sets
Ch3. Convex, PseudoConvex and QuasiConvex Functions

Part2 Optimality Conditions and Duality
Ch.4 The Fritz John and Karush-Kuhn-Tucker Optimality
Ch. 5 Constraint Qualifications
Ch. 6 Lagrangian Duality and Saddle Point Optimality Conditions

Part3 Algorithms and Their Convergence
Ch. 7 The Concept of an Algorithm (based on Zangwill work)
Ch. 8 Unconstrained Optimization (includes something about Trust Region)
Ch. 9 Penalty and Barrier Functions
Ch. 10 Methods of Feasible Directions
Ch. 11 Linear Complementary Problem, Quadratic, Separable, Fractional, and Geometric Programming

App. A Mathematical Review
App. B Summary of Convexity, Optimality Conditions, and Duality

-----------------------------

- Bu this edition as the second edition has several typos.
- a very good reference (up to date) for optimization courses.

This is a very good text for learning nonlinear programming. It expects that the reader has an understanding of linear algebra and mathematical sets but if you are prepared for a graduate NLP course then you'll find it accessible. It discusses how the problem formulation informs the type of algorithm best used to solve it as well as the algorithms themselves. As a graduate student, I highly recommend this book.