Interior Point Algorithms: Theory and Analysis [Hardcover]

Yinyu Ye (Author)

Book Description

Publication Date: August 11, 1997 | ISBN-10: 0471174203 | ISBN-13: 978-0471174202 | Edition: 1

The first comprehensive review of the theory and practice of one of today's most powerful optimization techniques.

The explosive growth of research into and development of interior point algorithms over the past two decades has significantly improved the complexity of linear programming and yielded some of today's most sophisticated computing techniques. This book offers a comprehensive and thorough treatment of the theory, analysis, and implementation of this powerful computational tool.

Interior Point Algorithms provides detailed coverage of all basic and advanced aspects of the subject. Beginning with an overview of fundamental mathematical procedures, Professor Yinyu Ye moves swiftly on to in-depth explorations of numerous computational problems and the algorithms that have been developed to solve them. An indispensable text/reference for students and researchers in applied mathematics, computer science, operations research, management science, and engineering, Interior Point Algorithms:
* Derives various complexity results for linear and convex programming
* Emphasizes interior point geometry and potential theory
* Covers state-of-the-art results for extension, implementation, and other cutting-edge computational techniques
* Explores the hottest new research topics, including nonlinear programming and nonconvex optimization.

Editorial Reviews

From the Publisher

This book describes the theory and analysis of interior-point algorithms, and explosive research development during the last ten years. It derives complexity results for linear and convex programming. Written in a style to motivate the reader, it provides state-of-the-art results which invoke computational techniques such as Matlab commands or generic algorithms. Contains future research topics for fractional programming and nonconvex (combinatorial) optimization.

From the Back Cover

The first comprehensive review of the theory and practice of one of today's most powerful optimization techniques.

The explosive growth of research into and development of interior point algorithms over the past two decades has significantly improved the complexity of linear programming and yielded some of today's most sophisticated computing techniques. This book offers a comprehensive and thorough treatment of the theory, analysis, and implementation of this powerful computational tool.

Interior Point Algorithms provides detailed coverage of all basic and advanced aspects of the subject. Beginning with an overview of fundamental mathematical procedures, Professor Yinyu Ye moves swiftly on to in-depth explorations of numerous computational problems and the algorithms that have been developed to solve them. An indispensable text/reference for students and researchers in applied mathematics, computer science, operations research, management science, and engineering, Interior Point Algorithms:

• Derives various complexity results for linear and convex programming
• Emphasizes interior point geometry and potential theory
• Covers state-of-the-art results for extension, implementation, and other cutting-edge computational techniques
• Explores the hottest new research topics, including nonlinear programming and nonconvex optimization.

See all Editorial Reviews

Product Details

• Hardcover: 440 pages
• Publisher: Wiley-Interscience; 1 edition (August 11, 1997)
• Language: English
• ISBN-10: 0471174203
• ISBN-13: 978-0471174202
• Product Dimensions: 9.6 x 6.4 x 1 inches
• Shipping Weight: 1.8 pounds (View shipping rates and policies)
• Average Customer Review: 4.0 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #3,409,820 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

4 of 4 people found the following review helpful:

4.0 out of 5 stars A rigorous account of Interior Point Methods, January 12, 2000

By 

KARTIK KRISHNAN S. - See all my reviews

This review is from: Interior Point Algorithms: Theory and Analysis (Hardcover)

Yinyu Ye is one of the exponents of Modern Day Interior Point Methods. He is responsible for a class of interior point methods called "Potential Reduction Methods", and you will find a good account of it in this book.

If you are looking for an introduction to interior point methods, I would rather recommend the books by Roos, Vial and Terlaky and Stephen Wright (in that order).

However Yinyu Ye's book certainly deserves a "looking over", if you wish to gain a mastery of interior point methods.

4 of 6 people found the following review helpful:

4.0 out of 5 stars Yes Good ! But !, August 13, 1999

By A Customer

This review is from: Interior Point Algorithms: Theory and Analysis (Hardcover)

Our times are as much complex as this book is. Of course Luenberger instinct and intiution is missing. But this book has taken a lot of the spirit of Luenberger way of writting and it should because the writer probably had this great man as a teacher. Unfortunately each paragraph is only C0 continue with the others. For instance chapter 4 seems to be independent of Chapter 3 despite the writer generous attempts to prevent us against. Couldn't it have been more illustrative in Karmarkar's algorithm for instance to be mentioned in a straight-forward manner that we first find a feasible point then find the analytic center of Omega which is a central-path point. Then we place the objective line passing this point, then minimizing to the analytic center of omega(z) then when |pk| < n < 1 then we have an 9/10 analytic center of it then we move the line to this center and then do the same job. The 'deeper cut' that is described does not convince because the movements of the objective line are fewer than other iterartions. Concluding this book should be treated as a guide to a wonderful new world. But theories of Interior - Point MUST be made more easy. I am sure that there exist Proofs and theorems that are more "simple" and thus more "reliable". Lets hope that a new Luenberger is on his way...