Nonlinear Conjugate Gradient Methods For Unconstrained Optimization PDF Download
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Author | : Neculai Andrei |
Publisher | : Springer Nature |
Total Pages | : 515 |
Release | : 2020-06-23 |
Genre | : Mathematics |
ISBN | : 3030429504 |
Download Nonlinear Conjugate Gradient Methods for Unconstrained Optimization Book in PDF, ePub and Kindle
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 |
Total Pages | : 486 |
Release | : 2020-06-29 |
Genre | : Mathematics |
ISBN | : 9783030429492 |
Download Nonlinear Conjugate Gradient Methods for Unconstrained Optimization Book in PDF, ePub and Kindle
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 | : Radoslaw Pytlak |
Publisher | : Springer Science & Business Media |
Total Pages | : 493 |
Release | : 2008-11-18 |
Genre | : Mathematics |
ISBN | : 354085634X |
Download Conjugate Gradient Algorithms in Nonconvex Optimization Book in PDF, ePub and Kindle
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 | : Christodoulos A. Floudas |
Publisher | : Springer Science & Business Media |
Total Pages | : 4646 |
Release | : 2008-09-04 |
Genre | : Mathematics |
ISBN | : 0387747583 |
Download Encyclopedia of Optimization Book in PDF, ePub and Kindle
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 | : S. V. Gopala Krishna |
Publisher | : |
Total Pages | : 254 |
Release | : 1971 |
Genre | : |
ISBN | : |
Download Nonlinear Optimization by the Sequential Unconstrained Minimization Technique Using Conjugate Gradient Methods Book in PDF, ePub and Kindle
Author | : Bhagwat Ram |
Publisher | : Springer Nature |
Total Pages | : 150 |
Release | : |
Genre | : |
ISBN | : 981972435X |
Download Unconstrained Optimization and Quantum Calculus Book in PDF, ePub and Kindle
Author | : Philip Wolfe |
Publisher | : |
Total Pages | : 564 |
Release | : 1970 |
Genre | : Programming (Mathematics). |
ISBN | : |
Download Integer and Nonlinear Programming Book in PDF, ePub and Kindle
A NATO Summer School held in Bandol, France, sponsored by the Scientific Affairs Division of NATO.
Author | : Neculai Andrei |
Publisher | : Springer |
Total Pages | : 514 |
Release | : 2017-12-04 |
Genre | : Mathematics |
ISBN | : 3319583565 |
Download Continuous Nonlinear Optimization for Engineering Applications in GAMS Technology Book in PDF, ePub and Kindle
This book presents the theoretical details and computational performances of algorithms used for solving continuous nonlinear optimization applications imbedded in GAMS. Aimed toward scientists and graduate students who utilize optimization methods to model and solve problems in mathematical programming, operations research, business, engineering, and industry, this book enables readers with a background in nonlinear optimization and linear algebra to use GAMS technology to understand and utilize its important capabilities to optimize algorithms for modeling and solving complex, large-scale, continuous nonlinear optimization problems or applications. Beginning with an overview of constrained nonlinear optimization methods, this book moves on to illustrate key aspects of mathematical modeling through modeling technologies based on algebraically oriented modeling languages. Next, the main feature of GAMS, an algebraically oriented language that allows for high-level algebraic representation of mathematical optimization models, is introduced to model and solve continuous nonlinear optimization applications. More than 15 real nonlinear optimization applications in algebraic and GAMS representation are presented which are used to illustrate the performances of the algorithms described in this book. Theoretical and computational results, methods, and techniques effective for solving nonlinear optimization problems, are detailed through the algorithms MINOS, KNITRO, CONOPT, SNOPT and IPOPT which work in GAMS technology.
Author | : Jorge Nocedal |
Publisher | : Springer Science & Business Media |
Total Pages | : 686 |
Release | : 2006-12-11 |
Genre | : Mathematics |
ISBN | : 0387400656 |
Download Numerical Optimization Book in PDF, ePub and Kindle
Optimization is an important tool used in decision science and for the analysis of physical systems used in engineering. One can trace its roots to the Calculus of Variations and the work of Euler and Lagrange. This natural and reasonable approach to mathematical programming covers numerical methods for finite-dimensional optimization problems. It begins with very simple ideas progressing through more complicated concepts, concentrating on methods for both unconstrained and constrained optimization.
Author | : Shashi Kant Mishra |
Publisher | : Springer Nature |
Total Pages | : 309 |
Release | : 2019-12-17 |
Genre | : Mathematics |
ISBN | : 9811508941 |
Download Introduction to Unconstrained Optimization with R Book in PDF, ePub and Kindle
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.