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Book An Accelerated Interior Point Method Whose Running Time Depends Only on A

Download or read book An Accelerated Interior Point Method Whose Running Time Depends Only on A written by Cornell University. Dept. of Computer Science and published by . This book was released on 1993 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose a ``layered-step'' interior point (LIP) algorithm for linear programming. This algorithm follows the central path, either with short steps or with a new type of step called a ``layered least squares'' (LLS) step. The algorithm returns the exact global minimum after a finite number of steps-in particular, after $O(n[superscript]{3.5}c(A))$ iterations, where $c(A)$ is a function of the coefficient matrix. The LLS steps can be thought of as accelerating a path-following interior point method whenever near-degeneracies occur. One consequence of the new method is a new characterization of the central path: we show that it composed of at most $n[superscript]2$ alternating straight and curved segments. If the LIP algorithm is applied to integer data, we get as another corollary a new proof of a well-known theorem by Tardos that linear programming can be solved in strongly polynomial time provided that $A$ contains small-integer entries.

Book Interior Point Methods of Mathematical Programming

Download or read book Interior Point Methods of Mathematical Programming written by Tamás Terlaky and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: One has to make everything as simple as possible but, never more simple. Albert Einstein Discovery consists of seeing what every body has seen and thinking what nobody has thought. Albert S. ent_Gyorgy; The primary goal of this book is to provide an introduction to the theory of Interior Point Methods (IPMs) in Mathematical Programming. At the same time, we try to present a quick overview of the impact of extensions of IPMs on smooth nonlinear optimization and to demonstrate the potential of IPMs for solving difficult practical problems. The Simplex Method has dominated the theory and practice of mathematical pro gramming since 1947 when Dantzig discovered it. In the fifties and sixties several attempts were made to develop alternative solution methods. At that time the prin cipal base of interior point methods was also developed, for example in the work of Frisch (1955), Caroll (1961), Huard (1967), Fiacco and McCormick (1968) and Dikin (1967). In 1972 Klee and Minty made explicit that in the worst case some variants of the simplex method may require an exponential amount of work to solve Linear Programming (LP) problems. This was at the time when complexity theory became a topic of great interest. People started to classify mathematical programming prob lems as efficiently (in polynomial time) solvable and as difficult (NP-hard) problems. For a while it remained open whether LP was solvable in polynomial time or not. The break-through resolution ofthis problem was obtained by Khachijan (1989).

Book Modeling And Computations In Dynamical Systems In Commemoration Of The 100th Anniversary Of The Birth Of John Von Neumann

Download or read book Modeling And Computations In Dynamical Systems In Commemoration Of The 100th Anniversary Of The Birth Of John Von Neumann written by Eusebius Doedel and published by World Scientific. This book was released on 2006-03-10 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Hungarian born mathematical genius, John von Neumann, was undoubtedly one of the greatest and most influential scientific minds of the 20th century. Von Neumann made fundamental contributions to Computing and he had a keen interest in Dynamical Systems, specifically Hydrodynamic Turbulence. This book, offering a state-of-the-art collection of papers in computational dynamical systems, is dedicated to the memory of von Neumann. Including contributions from J E Marsden, P J Holmes, M Shub, A Iserles, M Dellnitz and J Guckenheimer, this book offers a unique combination of theoretical and applied research in areas such as geometric integration, neural networks, linear programming, dynamical astronomy, chemical reaction models, structural and fluid mechanics.The contents of this book was also published as a special issue of the International Journal of Bifurcation and Chaos — March 2005.

Book Stable and Efficient Solution of Weighted Least squares Problems with Applications in Interior Point Methods

Download or read book Stable and Efficient Solution of Weighted Least squares Problems with Applications in Interior Point Methods written by Patricia D. Hough and published by . This book was released on 1996 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book Interior point Polynomial Algorithms in Convex Programming

Download or read book Interior point Polynomial Algorithms in Convex Programming written by Yurii Nesterov and published by SIAM. This book was released on 1994-01-01 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: Specialists working in the areas of optimization, mathematical programming, or control theory will find this book invaluable for studying interior-point methods for linear and quadratic programming, polynomial-time methods for nonlinear convex programming, and efficient computational methods for control problems and variational inequalities. A background in linear algebra and mathematical programming is necessary to understand the book. The detailed proofs and lack of "numerical examples" might suggest that the book is of limited value to the reader interested in the practical aspects of convex optimization, but nothing could be further from the truth. An entire chapter is devoted to potential reduction methods precisely because of their great efficiency in practice.

Book Numerical Methods in Applied Sciences

Download or read book Numerical Methods in Applied Sciences written by Wei Cai and published by . This book was released on 1996 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book Calculation of Pseudospectra by the Arnoldi Iteration

Download or read book Calculation of Pseudospectra by the Arnoldi Iteration written by Kim Chuan Toh and published by . This book was released on 1994 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book Capacitated Planned Maintenance

Download or read book Capacitated Planned Maintenance written by Torben Kuschel and published by Springer. This book was released on 2016-11-08 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book examines the problem of maintenance planning and scheduling in industrial production systems. It presents two practically relevant, deterministic mathematical models: the capacitated planned maintenance problem (CPMP) and the weighted uncapacitated planned maintenance problem (WUPMP). It introduces specific optimization algorithms such as construction heuristics, Lagrangean and tabu search metaheuristics. A problem independent hybrid approach links and alternates between two Lagrangean relaxations. It also analyzes the solvability with respect to the computational complexity of several problem classes, polyhedral properties and lower bounds. Computational studies demonstrate the performance of the heuristics, lower bounds, subgradients obtained from heuristics and the quality of dual information. This unique book includes implementation details and an introduction to the necessary theory making it suitable for upper undergraduate students.

Book Modifying a Rank revealing ULLV Decomposition

Download or read book Modifying a Rank revealing ULLV Decomposition written by James Michael Lebak and published by . This book was released on 1994 with total page 62 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book Advanced Computing Research Institute

Download or read book Advanced Computing Research Institute written by Keshav Pingali and published by . This book was released on 1994 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book Proceedings of the Twenty sixth Annual ACM Symposium on the Theory of Computing

Download or read book Proceedings of the Twenty sixth Annual ACM Symposium on the Theory of Computing written by and published by Association for Computing Machinery (ACM). This book was released on 1994 with total page 836 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book Getting CUTE with Matlab

Download or read book Getting CUTE with Matlab written by Mary Ann Branch and published by . This book was released on 1994 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book Advanced Computing Research Institute

Download or read book Advanced Computing Research Institute written by and published by . This book was released on 1993 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: