Romesh Saigal - Böcker
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4 produkter
4 produkter
Del 27 - International Series in Operations Research & Management Science
Handbook of Semidefinite Programming
Theory, Algorithms, and Applications
Inbunden, Engelska, 2000
2 416 kr
Skickas inom 10-15 vardagar
Semidefinite programming (SDP) is one of the research areas in optimization. It has and continues to attract researchers with very diverse backgrounds, including experts in convex programming, linear algebra, numerical optimization, combinatorial optimization, control theory, and statistics. This research activity has been prompted by the discovery of applications in combinatorial optimization and control theory, the development of efficient interior-point algorithms for solving SDP problems, and the depth and elegance of the underlying optimization theory. This handbook offers an advanced and broad overview of the field. It contains 19 chapters organized in three parts: theory, algorithms, and applications and extensions.
2 101 kr
Skickas inom 10-15 vardagar
In this study, both boundary (simplex) and interior point methods are derived from the complementary slackness theorem, and 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 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. A 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.
Del 1 - International Series in Operations Research & Management Science
Linear Programming
A Modern Integrated Analysis
Häftad, Engelska, 2012
2 311 kr
Skickas inom 10-15 vardagar
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.
Del 27 - International Series in Operations Research & Management Science
Handbook of Semidefinite Programming
Theory, Algorithms, and Applications
Häftad, Engelska, 2012
2 416 kr
Skickas inom 10-15 vardagar
This tremendous research activity has been prompted by the discovery of important applications in combinatorial optimization and control theory, the development of efficient interior-point algorithms for solving SDP problems, and the depth and elegance of the underlying optimization theory.