{"product_id":"9780792396222","title":"International Series in Operations Research \u0026 Management Science: A Modern Integrated Analysis","description":"\u003ch1\u003eInternational Series in Operations Research \u0026amp; Management Science: A Modern Integrated Analysis\u003c\/h1\u003e \u003ch2\u003eSaigal, Romesh\u003c\/h2\u003e \u003cp\u003eIn \u003cem\u003eLinear Programming: A Modern Integrated Analysis\u003c\/em\u003e, both  boundary (simplex) and interior point methods are derived from the  complementary slackness theorem and, unlike most books, the duality  theorem is derived from Farkas's Lemma, which is proved as a convex  separation theorem. The tedium of the simplex method is thus avoided.  \u003cbr\u003e  A new and inductive proof of Kantorovich's Theorem is offered, related  to the convergence of Newton's method. Of the boundary methods, the  book presents the (revised) primal and the dual simplex methods. An  extensive discussion is given of the primal, dual and primal-dual  affine scaling methods. In addition, the proof of the convergence  under degeneracy, a bounded variable variant, and a super-linearly  convergent variant of the primal affine scaling method are covered in  one chapter. Polynomial barrier or path-following homotopy methods,  and the projective transformation method are also covered in the  interior point chapter. Besides the popular sparse Cholesky  factorization and the conjugate gradient method, new methods are  presented in a separate chapter on implementation. These methods use  LQ factorization and iterative techniques. \u003cbr\u003e\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 1995-11-30\u003c\/p\u003e \u003cp\u003eFormat: Hardcover\u003c\/p\u003e \u003cp\u003eISBN-13: 9780792396222\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-1-4615-2311-6\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 342\u003c\/p\u003e ","brand":"Springer US","offers":[{"title":"Default Title","offer_id":45378471002252,"sku":"9780792396222","price":197.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9780792396222.jpg?v=1775004562","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9780792396222","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}