Average Reviews:
(More customer reviews)The book meets the need for a teacher/research worker in LP theory, given the modern developments after development of Karmarkar's interior point approaches. The chapter 2 gives the basic background about analysis & numerical linear algebra. It makes duality as central theme. ( It differs from earlier OR books, where duality is introduced after simplex algorithm discussed). It is interesting to note the amount of attention paid to the issue of degeneracy. This is the special aspect of the book. The author discusses the interior point methods in a very systmeatic way; giving the necessary proofs. Last chapter discusses the implementation issues. Interestingly, the book has no figures, no diagramms. May the author is against use of them. The author could have given more details about Korbx, or the solvers available ( like AMPL, public domain interior point solvers), so that the reader is made aware the concepts dealt in the book is useful even for users of LP.
Click Here to see more reviews about: Linear Programming: A Modern Integrated Analysis (International Series in Operations Research & Management Science)
In Linear Programming: A Modern Integrated Analysis, bothboundary (simplex) and interior point methods are derived from thecomplementary slackness theorem and, unlike most books, the dualitytheorem is derived from Farkas's Lemma, which is proved as a convexseparation theorem. The tedium of the simplex method is thus avoided.A new and inductive proof of Kantorovich's Theorem is offered, relatedto the convergence of Newton's method. Of the boundary methods, thebook presents the (revised) primal and the dual simplex methods. Anextensive discussion is given of the primal, dual and primal-dualaffine scaling methods. In addition, the proof of the convergenceunder degeneracy, a bounded variable variant, and a super-linearlyconvergent variant of the primal affine scaling method are covered inone chapter. Polynomial barrier or path-following homotopy methods,and the projective transformation method are also covered in theinterior point chapter. Besides the popular sparse Choleskyfactorization and the conjugate gradient method, new methods arepresented in a separate chapter on implementation. These methods useLQ factorization and iterative techniques.
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