Nonlinear Conjugate Gradient Methods For Unconstrained Optimization

Author : Neculai Andrei
Publisher : Springer
Page : 486 pages
File Size : 40,9 Mb
Release : 2020-06-29
Category : Mathematics
ISBN : 3030429490

Get Book

Nonlinear Conjugate Gradient Methods for Unconstrained Optimization by Neculai Andrei Pdf

Two approaches are known for solving large-scale unconstrained optimization problems—the limited-memory quasi-Newton method (truncated Newton method) and the conjugate gradient method. This is the first book to detail conjugate gradient methods, showing their properties and convergence characteristics as well as their performance in solving large-scale unconstrained optimization problems and applications. Comparisons to the limited-memory and truncated Newton methods are also discussed. Topics studied in detail include: linear conjugate gradient methods, standard conjugate gradient methods, acceleration of conjugate gradient methods, hybrid, modifications of the standard scheme, memoryless BFGS preconditioned, and three-term. Other conjugate gradient methods with clustering the eigenvalues or with the minimization of the condition number of the iteration matrix, are also treated. For each method, the convergence analysis, the computational performances and the comparisons versus other conjugate gradient methods are given. The theory behind the conjugate gradient algorithms presented as a methodology is developed with a clear, rigorous, and friendly exposition; the reader will gain an understanding of their properties and their convergence and will learn to develop and prove the convergence of his/her own methods. Numerous numerical studies are supplied with comparisons and comments on the behavior of conjugate gradient algorithms for solving a collection of 800 unconstrained optimization problems of different structures and complexities with the number of variables in the range [1000,10000]. The book is addressed to all those interested in developing and using new advanced techniques for solving unconstrained optimization complex problems. Mathematical programming researchers, theoreticians and practitioners in operations research, practitioners in engineering and industry researchers, as well as graduate students in mathematics, Ph.D. and master students in mathematical programming, will find plenty of information and practical applications for solving large-scale unconstrained optimization problems and applications by conjugate gradient methods.

Author : Neculai Andrei
Publisher : Springer Nature
Page : 515 pages
File Size : 41,9 Mb
Release : 2020-06-23
Category : Mathematics
ISBN : 9783030429508

Get Book

Nonlinear Conjugate Gradient Methods for Unconstrained Optimization by Neculai Andrei Pdf

Two approaches are known for solving large-scale unconstrained optimization problems—the limited-memory quasi-Newton method (truncated Newton method) and the conjugate gradient method. This is the first book to detail conjugate gradient methods, showing their properties and convergence characteristics as well as their performance in solving large-scale unconstrained optimization problems and applications. Comparisons to the limited-memory and truncated Newton methods are also discussed. Topics studied in detail include: linear conjugate gradient methods, standard conjugate gradient methods, acceleration of conjugate gradient methods, hybrid, modifications of the standard scheme, memoryless BFGS preconditioned, and three-term. Other conjugate gradient methods with clustering the eigenvalues or with the minimization of the condition number of the iteration matrix, are also treated. For each method, the convergence analysis, the computational performances and the comparisons versus other conjugate gradient methods are given. The theory behind the conjugate gradient algorithms presented as a methodology is developed with a clear, rigorous, and friendly exposition; the reader will gain an understanding of their properties and their convergence and will learn to develop and prove the convergence of his/her own methods. Numerous numerical studies are supplied with comparisons and comments on the behavior of conjugate gradient algorithms for solving a collection of 800 unconstrained optimization problems of different structures and complexities with the number of variables in the range [1000,10000]. The book is addressed to all those interested in developing and using new advanced techniques for solving unconstrained optimization complex problems. Mathematical programming researchers, theoreticians and practitioners in operations research, practitioners in engineering and industry researchers, as well as graduate students in mathematics, Ph.D. and master students in mathematical programming, will find plenty of information and practical applications for solving large-scale unconstrained optimization problems and applications by conjugate gradient methods.

Author : Bhagwat Ram
Publisher : Springer Nature
Page : 150 pages
File Size : 51,5 Mb
Release : 2024-06-26
Category : Electronic
ISBN : 9789819724352

Get Book

Unconstrained Optimization and Quantum Calculus by Bhagwat Ram Pdf

Author : Radoslaw Pytlak
Publisher : Springer Science & Business Media
Page : 493 pages
File Size : 41,5 Mb
Release : 2008-11-18
Category : Mathematics
ISBN : 9783540856344

Get Book

Conjugate Gradient Algorithms in Nonconvex Optimization by Radoslaw Pytlak Pdf

This book details algorithms for large-scale unconstrained and bound constrained optimization. It shows optimization techniques from a conjugate gradient algorithm perspective as well as methods of shortest residuals, which have been developed by the author.

Author : Neculai Andrei
Publisher : Springer Nature
Page : 126 pages
File Size : 41,6 Mb
Release : 2021-03-31
Category : Mathematics
ISBN : 9783030685171

Get Book

A Derivative-free Two Level Random Search Method for Unconstrained Optimization by Neculai Andrei Pdf

The book is intended for graduate students and researchers in mathematics, computer science, and operational research. The book presents a new derivative-free optimization method/algorithm based on randomly generated trial points in specified domains and where the best ones are selected at each iteration by using a number of rules. This method is different from many other well established methods presented in the literature and proves to be competitive for solving many unconstrained optimization problems with different structures and complexities, with a relative large number of variables. Intensive numerical experiments with 140 unconstrained optimization problems, with up to 500 variables, have shown that this approach is efficient and robust. Structured into 4 chapters, Chapter 1 is introductory. Chapter 2 is dedicated to presenting a two level derivative-free random search method for unconstrained optimization. It is assumed that the minimizing function is continuous, lower bounded and its minimum value is known. Chapter 3 proves the convergence of the algorithm. In Chapter 4, the numerical performances of the algorithm are shown for solving 140 unconstrained optimization problems, out of which 16 are real applications. This shows that the optimization process has two phases: the reduction phase and the stalling one. Finally, the performances of the algorithm for solving a number of 30 large-scale unconstrained optimization problems up to 500 variables are presented. These numerical results show that this approach based on the two level random search method for unconstrained optimization is able to solve a large diversity of problems with different structures and complexities. There are a number of open problems which refer to the following aspects: the selection of the number of trial or the number of the local trial points, the selection of the bounds of the domains where the trial points and the local trial points are randomly generated and a criterion for initiating the line search.

Author : Shashi Kant Mishra,Bhagwat Ram
Publisher : Springer Nature
Page : 309 pages
File Size : 43,9 Mb
Release : 2019-12-17
Category : Mathematics
ISBN : 9789811508943

Get Book

Introduction to Unconstrained Optimization with R by Shashi Kant Mishra,Bhagwat Ram Pdf

This book discusses unconstrained optimization with R—a free, open-source computing environment, which works on several platforms, including Windows, Linux, and macOS. The book highlights methods such as the steepest descent method, Newton method, conjugate direction method, conjugate gradient methods, quasi-Newton methods, rank one correction formula, DFP method, BFGS method and their algorithms, convergence analysis, and proofs. Each method is accompanied by worked examples and R scripts. To help readers apply these methods in real-world situations, the book features a set of exercises at the end of each chapter. Primarily intended for graduate students of applied mathematics, operations research and statistics, it is also useful for students of mathematics, engineering, management, economics, and agriculture.

Author : Neculai Andrei
Publisher : Springer Nature
Page : 824 pages
File Size : 50,5 Mb
Release : 2022-10-18
Category : Mathematics
ISBN : 9783031087202

Get Book

Modern Numerical Nonlinear Optimization by Neculai Andrei Pdf

This book includes a thorough theoretical and computational analysis of unconstrained and constrained optimization algorithms and combines and integrates the most recent techniques and advanced computational linear algebra methods. Nonlinear optimization methods and techniques have reached their maturity and an abundance of optimization algorithms are available for which both the convergence properties and the numerical performances are known. This clear, friendly, and rigorous exposition discusses the theory behind the nonlinear optimization algorithms for understanding their properties and their convergence, enabling the reader to prove the convergence of his/her own algorithms. It covers cases and computational performances of the most known modern nonlinear optimization algorithms that solve collections of unconstrained and constrained optimization test problems with different structures, complexities, as well as those with large-scale real applications. The book is addressed to all those interested in developing and using new advanced techniques for solving large-scale unconstrained or constrained complex optimization problems. Mathematical programming researchers, theoreticians and practitioners in operations research, practitioners in engineering and industry researchers, as well as graduate students in mathematics, Ph.D. and master in mathematical programming will find plenty of recent information and practical approaches for solving real large-scale optimization problems and applications.

Author : Christodoulos A. Floudas,Panos M. Pardalos
Publisher : Springer Science & Business Media
Page : 4646 pages
File Size : 51,7 Mb
Release : 2008-09-04
Category : Mathematics
ISBN : 9780387747583

Get Book

Encyclopedia of Optimization by Christodoulos A. Floudas,Panos M. Pardalos Pdf

The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field. The second edition builds on the success of the former edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as "Algorithms for Genomics", "Optimization and Radiotherapy Treatment Design", and "Crew Scheduling".

Author : Roger Fletcher
Publisher : John Wiley & Sons
Page : 136 pages
File Size : 48,9 Mb
Release : 1986
Category : Mathematics
ISBN : UOM:39015010639105

Get Book

Practical Methods of Optimization: Unconstrained optimization by Roger Fletcher Pdf

Author : Philip Wolfe
Publisher : Unknown
Page : 564 pages
File Size : 51,7 Mb
Release : 1970
Category : Programming (Mathematics).
ISBN : UOM:39015017343743

Get Book

Integer and Nonlinear Programming by Philip Wolfe Pdf

A NATO Summer School held in Bandol, France, sponsored by the Scientific Affairs Division of NATO.

Author : Loyce M. Adams,John Lawrence Nazareth
Publisher : SIAM
Page : 186 pages
File Size : 42,9 Mb
Release : 1996-01-01
Category : Mathematics
ISBN : 0898713765

Get Book

Linear and Nonlinear Conjugate Gradient-related Methods by Loyce M. Adams,John Lawrence Nazareth Pdf

Proceedings of the AMS-IMS-SIAM Summer Research Conference held at the University of Washington, July 1995.

Author : R. Fletcher
Publisher : John Wiley & Sons
Page : 470 pages
File Size : 54,8 Mb
Release : 2013-06-06
Category : Mathematics
ISBN : 9781118723180

Get Book

Practical Methods of Optimization by R. Fletcher Pdf

Fully describes optimization methods that are currently most valuable in solving real-life problems. Since optimization has applications in almost every branch of science and technology, the text emphasizes their practical aspects in conjunction with the heuristics useful in making them perform more reliably and efficiently. To this end, it presents comparative numerical studies to give readers a feel for possibile applications and to illustrate the problems in assessing evidence. Also provides theoretical background which provides insights into how methods are derived. This edition offers revised coverage of basic theory and standard techniques, with updated discussions of line search methods, Newton and quasi-Newton methods, and conjugate direction methods, as well as a comprehensive treatment of restricted step or trust region methods not commonly found in the literature. Also includes recent developments in hybrid methods for nonlinear least squares; an extended discussion of linear programming, with new methods for stable updating of LU factors; and a completely new section on network programming. Chapters include computer subroutines, worked examples, and study questions.

Author : Jorge Nocedal,Stephen Wright
Publisher : Springer Science & Business Media
Page : 636 pages
File Size : 41,6 Mb
Release : 2006-06-06
Category : Mathematics
ISBN : 9780387227429

Get Book

Numerical Optimization by Jorge Nocedal,Stephen Wright Pdf

The new edition of this book presents a comprehensive and up-to-date description of the most effective methods in continuous optimization. It responds to the growing interest in optimization in engineering, science, and business by focusing on methods best suited to practical problems. This edition has been thoroughly updated throughout. There are new chapters on nonlinear interior methods and derivative-free methods for optimization, both of which are widely used in practice and are the focus of much current research. Because of the emphasis on practical methods, as well as the extensive illustrations and exercises, the book is accessible to a wide audience.

Author : Andrzej Ruszczynski
Publisher : Princeton University Press
Page : 464 pages
File Size : 45,9 Mb
Release : 2011-09-19
Category : Mathematics
ISBN : 9781400841059

Get Book

Nonlinear Optimization by Andrzej Ruszczynski Pdf

Optimization is one of the most important areas of modern applied mathematics, with applications in fields from engineering and economics to finance, statistics, management science, and medicine. While many books have addressed its various aspects, Nonlinear Optimization is the first comprehensive treatment that will allow graduate students and researchers to understand its modern ideas, principles, and methods within a reasonable time, but without sacrificing mathematical precision. Andrzej Ruszczynski, a leading expert in the optimization of nonlinear stochastic systems, integrates the theory and the methods of nonlinear optimization in a unified, clear, and mathematically rigorous fashion, with detailed and easy-to-follow proofs illustrated by numerous examples and figures. The book covers convex analysis, the theory of optimality conditions, duality theory, and numerical methods for solving unconstrained and constrained optimization problems. It addresses not only classical material but also modern topics such as optimality conditions and numerical methods for problems involving nondifferentiable functions, semidefinite programming, metric regularity and stability theory of set-constrained systems, and sensitivity analysis of optimization problems. Based on a decade's worth of notes the author compiled in successfully teaching the subject, this book will help readers to understand the mathematical foundations of the modern theory and methods of nonlinear optimization and to analyze new problems, develop optimality theory for them, and choose or construct numerical solution methods. It is a must for anyone seriously interested in optimization.

Author : M.R. Hestenes
Publisher : Springer Science & Business Media
Page : 334 pages
File Size : 49,7 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461260486

Get Book

Conjugate Direction Methods in Optimization by M.R. Hestenes Pdf

Shortly after the end of World War II high-speed digital computing machines were being developed. It was clear that the mathematical aspects of com putation needed to be reexamined in order to make efficient use of high-speed digital computers for mathematical computations. Accordingly, under the leadership of Min a Rees, John Curtiss, and others, an Institute for Numerical Analysis was set up at the University of California at Los Angeles under the sponsorship of the National Bureau of Standards. A similar institute was formed at the National Bureau of Standards in Washington, D. C. In 1949 J. Barkeley Rosser became Director of the group at UCLA for a period of two years. During this period we organized a seminar on the study of solu tions of simultaneous linear equations and on the determination of eigen values. G. Forsythe, W. Karush, C. Lanczos, T. Motzkin, L. J. Paige, and others attended this seminar. We discovered, for example, that even Gaus sian elimination was not well understood from a machine point of view and that no effective machine oriented elimination algorithm had been developed. During this period Lanczos developed his three-term relationship and I had the good fortune of suggesting the method of conjugate gradients. We dis covered afterward that the basic ideas underlying the two procedures are essentially the same. The concept of conjugacy was not new to me. In a joint paper with G. D.