Customer Reviews

Interior Point Algorithms: Theory and Analysis

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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.

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...