Linear Programming: A Modern Integrated Analysis
Romesh Saigal
2012年12月 · International Series in Operations Research & Management Science 1 巻 · Springer Science & Business Media
4.0star
2 件のレビューreport
電子書籍
342
ページ
report評価とレビューは確認済みではありません 詳細
この電子書籍について
In Linear Programming: A Modern Integrated Analysis, 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.
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.
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.
評価とレビュー
4.0
2 件のレビュー
この電子書籍を評価する
ご感想をお聞かせください。
読書情報
スマートフォンとタブレット
Android や iPad / iPhone 用の Google Play ブックス アプリをインストールしてください。このアプリがアカウントと自動的に同期するため、どこでもオンラインやオフラインで読むことができます。
ノートパソコンとデスクトップ パソコン
Google Play で購入したオーディブックは、パソコンのウェブブラウザで再生できます。
電子書籍リーダーなどのデバイス
Kobo 電子書籍リーダーなどの E Ink デバイスで読むには、ファイルをダウンロードしてデバイスに転送する必要があります。サポートされている電子書籍リーダーにファイルを転送する方法について詳しくは、ヘルプセンターをご覧ください。
