Download or read book Parallel Methods for Unconstrained Optimization written by Charles Herbert Still and published by . This book was released on 1990 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Sequential and Parallel Methods for Unconstrained Optimization written by University of Colorado. Dept. of Computer Science and published by . This book was released on 1988 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper reviews some interesting recent developments in the field of unconstrained optimization. First we discuss some recent research regarding secant (quasi-Newton) methods. This includes analysis that has led to an improved understanding of the comparative behavior of the BFGS, DFP, and other updates in the Broyden class, as well as computational and theoretical work that has led to a revival of interest in the symmetric rank one update. Second we discuss recent research in methods that utilize second derivatives. We describe tensor methods for unconstrained optimization, which have achieved considerable gains in efficiency by augmenting the standard quadratic model with low rank third and fourth order terms, in order to allow the model to interpolate some function and gradient information from previous iterations. Finally, we will review some work that has been done in constructing general purpose methods for solving unconstrained optimization problems on parallel computers. This research has led to a renewed interest in various ways of performing the linear algebra computations in secant methods, and to new algorithms that make use of multiple concurrent function evaluations. (kr).

Download or read book Parallel Quasi Newton Methods for Unconstrained Optimization written by University of Colorado. Dept. of Computer Science and published by . This book was released on 1988 with total page 41 pages. Available in PDF, EPUB and Kindle. Book excerpt: This document discusses methods for solving the unconstrained optimization problem on parallel computers, when the number of variables is sufficiently small that quasi-Newton methods can be used. The authors concentrate mainly, but not exclusively, on problems where function evaluation is expensive. First they discuss ways to parallelize both the function evaluation costs and the linear algebra calculations in the standard sequential secant method, the BFGS method. Then described are new methods that are appropriate when there are enough processors to evaluate the function, gradient, and part but not all of the Hessian at each iteration. Developed are new algorithms that utilize this information and analyze their convergence properties. The authors present computational experiments showing that they are superior to parallelization of either the BFGS method or Newton's method under our assumptions on the number of processors and cost of function evaluation. Finally they discuss ways to effectively utilize the gradient values at unsuccessful trial points that are available in our parallel methods and also in some sequential software packages.

Download or read book Multi directional Parallel Algorithms for Unconstrained Optimization written by National University of Singapore. Dept. of Information Systems and Computer Science and published by . This book was released on 1993 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "Parallel algorithms for solving unconstrained nonlinear optimization problems are presented. These algorithms are based on the quasi-Newton methods. At each step of the algorithms, several search directions are generated in parallel using various quasi-Newton updates. Our numerical results show significant improvement in the number of iterations and function evaluations required by the parallel algorithms over those required by the serial quasi-Newton updates such as the SR1 method or the BFGS method for many of the test problems."

Download or read book Parallel Projected Variable Metric Algorithms for Unconstrained Optimization written by Institute for Computer Applications in Science and Engineering and published by . This book was released on 1989 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Parallel and Distributed Computation Numerical Methods written by Dimitri Bertsekas and published by Athena Scientific. This book was released on 2015-03-01 with total page 832 pages. Available in PDF, EPUB and Kindle. Book excerpt: This highly acclaimed work, first published by Prentice Hall in 1989, is a comprehensive and theoretically sound treatment of parallel and distributed numerical methods. It focuses on algorithms that are naturally suited for massive parallelization, and it explores the fundamental convergence, rate of convergence, communication, and synchronization issues associated with such algorithms. This is an extensive book, which aside from its focus on parallel and distributed algorithms, contains a wealth of material on a broad variety of computation and optimization topics. It is an excellent supplement to several of our other books, including Convex Optimization Algorithms (Athena Scientific, 2015), Nonlinear Programming (Athena Scientific, 1999), Dynamic Programming and Optimal Control (Athena Scientific, 2012), Neuro-Dynamic Programming (Athena Scientific, 1996), and Network Optimization (Athena Scientific, 1998). The on-line edition of the book contains a 95-page solutions manual.

Download or read book Parallel Unconstrained Optimization Methods written by F. A. Lootsma and published by . This book was released on 1984 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Self scaling Parallel Quasi Newton Methods for Nonlinear Unconstrained Optimization written by Weiguo Fan and published by . This book was released on 1997 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Parallel Optimization written by Yair Censor and published by Oxford University Press, USA. This book was released on 1997 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a unique pathway to methods of parallel optimization by introducing parallel computing ideas into both optimization theory and into some numerical algorithms for large-scale optimization problems. The three parts of the book bring together relevant theory, careful study of algorithms, and modeling of significant real world problems such as image reconstruction, radiation therapy treatment planning, financial planning, transportation and multi-commodity network flow problems, planning under uncertainty, and matrix balancing problems.

Download or read book Parallel Nonlinear Optimization Limitations Opportunities and Challenges written by and published by . This book was released on 1994 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt: The availability and power of parallel computers is having a significant impact on how large-scale problems are solved in all areas of numerical computation, and is likely to have an even larger impact in the future. This paper attempts to give some indication of how the consideration of parallel computation is affecting, and is likely to affect, the field of nonlinear optimization. It does not attempt to survey the research that has been done in parallel nonlinear optimization. Rather it presents a set of examples, mainly from our own research, that is intended to illustrate many of the limitations, opportunities, and challenges inherent in incorporating parallelism into the field of nonlinear optimization. These examples include parallel methods for small to medium size unconstrained optimization problems, parallel methods for large block bordered systems of nonlinear equations, and parallel methods for both small and large-scale global optimization problems. Our overall conclusions are mixed. For generic, small to medium size problems, the consideration of parallelism does not appear to be leading to major algorithmic innovations. For many classes of large-scale problems, however, the consideration of parallelism appears to be creating opportunities for the development of interesting new methods that may be advantageous for parallel and possibly even sequential computation. In addition, a number of large-scale parallel optimization algorithms exhibit irregular coarse-grain structure, which leads to interesting computer science challenges in their implementation.

Download or read book Parallel Algorithms for Unconstrained and Constrained Nonlinear Optimization written by F. A. Lootsma and published by . This book was released on 1986 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Parallel algorithms for large scale nonlinear optimization written by Kang Hoh Phua and published by . This book was released on 1996 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "Multi-step, multi-directional parallel variable metric (PVM) methods for unconstrained optimization problems are presented in this paper. These algorithms generate several VM directions at each iteration, different line search and scaling strategies are then applied in parallel along each search direction. In comparison to some serial VM methods, computational results show that a reduction of 200% or more in terms of number of iterations and function/gradient evaluations respectively could be achieved by the new parallel algorithm over a wide range of 63 test problems. In particular, when the complexity, or the size of the problem increases, greater savings could be achieved by the proposed parallel algorithm. In fact, the speedup factors gained by our PVM algorithms could be as high as 28 times for some test problems."

Download or read book Applications of Conjugate Directions and Quasi Newton Methods in Parallel Unconstrained Optimization written by Prapasri Asawakun and published by . This book was released on 1989 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Parallel Quasi newton Algorithms for Large scale Optimization written by National University of Singapore. Dept. of Information Systems and Computer Science and published by . This book was released on 1995 with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "Multi-step, multi-directional parallel quasi-Newton (QN) methods for unconstrained optimization problems are presented in this paper. These algorithms generate several QN directions at each iteration, different line search strategies are then applied in parallel along each search direction. Numerical experiments are carried out over a wide range of standard test functions. Computational results show that a reduction of 94% and 70% in the number of iterations and function/gradient evaluations respectively could be achieved by the new parallel algorithm. Furthermore, a speedup factor of 1.69 in CPU time could also be realized comparing with serial QN methods."

Download or read book Parallel Computing and Mathematical Optimization written by Manfred Grauer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: This special volume contains the Proceedings of a Workshop on "Parallel Algorithms and Transputers for Optimization" which was held at the University of Siegen, on November 9, 1990. The purpose of the Workshop was to bring together those doing research on 2.lgorithms for parallel and distributed optimization and those representatives from industry and business who have an increasing demand for computing power and who may be the potential users of nonsequential approaches. In contrast to many other conferences, especially North-American, on parallel processing and supercomputers the main focus of the contributions and discussion was "problem oriented". This view reflects the following philosophy: How can the existing computing infrastructure (PC's, workstations, local area networks) of an institution or a company be used for parallel and/or distributed problem solution in optimization. This volume of the LECfURE NOTES ON ECONOMICS AND MA THEMA TICAL SYSTEMS contains most of the papers presented at the workshop, plus some additional invited papers covering other important topics related to this workshop. The papers appear here grouped according to four general areas. (1) Solution of optimization problems using massive parallel systems (data parallelism). The authors of these papers are: Lootsma; Gehne. (II) Solution of optimization problems using coarse-grained parallel approaches on multiprocessor systems (control parallelism). The authors of these papers are: Bierwirth, Mattfeld, and Stoppler; Schwartz; Boden, Gehne, and Grauer; and Taudes and Netousek.

Download or read book Numerical Methods for Unconstrained Optimization and Nonlinear Equations written by J. E. Dennis, Jr. and published by SIAM. This book was released on 1996-12-01 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book has become the standard for a complete, state-of-the-art description of the methods for unconstrained optimization and systems of nonlinear equations. Originally published in 1983, it provides information needed to understand both the theory and the practice of these methods and provides pseudocode for the problems. The algorithms covered are all based on Newton's method or "quasi-Newton" methods, and the heart of the book is the material on computational methods for multidimensional unconstrained optimization and nonlinear equation problems. The republication of this book by SIAM is driven by a continuing demand for specific and sound advice on how to solve real problems. The level of presentation is consistent throughout, with a good mix of examples and theory, making it a valuable text at both the graduate and undergraduate level. It has been praised as excellent for courses with approximately the same name as the book title and would also be useful as a supplemental text for a nonlinear programming or a numerical analysis course. Many exercises are provided to illustrate and develop the ideas in the text. A large appendix provides a mechanism for class projects and a reference for readers who want the details of the algorithms. Practitioners may use this book for self-study and reference. For complete understanding, readers should have a background in calculus and linear algebra. The book does contain background material in multivariable calculus and numerical linear algebra.

Download or read book Using Parallel Function Evaluations to Improve Hessian Approximations for Unconstrained Optimization written by Richard H. Byrd and published by . This book was released on 1987 with total page 43 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper presents a new class of methods for solving unconstrained optimization problems on parallel computers. The methods are intended to solve small to moderate dimensional problems where function and derivative evaluation is the dominant cost. They utilize multiple processors to evaluate the function, (finite difference) gradient, and a portion of the finite difference Hessian simultaneously at each iterate. We introduce three types of new methods, which all utilize the new finite difference Hessian information in forming the new Hessian approximation at each iteration; they differ in whether and how they utilize the standard secant information from the current step as well. We present theoretical analyses of the rate of convergence of several of these methods. We also present computational results which illustrate their performance on parallel computers when function evaluation is expensive.