Methods For Unconstrained Optimization Problems
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Methods For Unconstrained Optimization Problems
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Author : Janusz S. Kowalik
language : en
Publisher: Elsevier Publishing Company
Release Date : 1968
Methods For Unconstrained Optimization Problems written by Janusz S. Kowalik and has been published by Elsevier Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Mathematics categories.
Methods For Unconstrained Optimization Problems
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Author : Janusz Szczesny Kowalik
language : en
Publisher:
Release Date : 1968
Methods For Unconstrained Optimization Problems written by Janusz Szczesny Kowalik and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Mathematical optimization categories.
Numerical Methods For Unconstrained Optimization And Nonlinear Equations
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Author : J. E. Dennis, Jr.
language : en
Publisher: SIAM
Release Date : 1996-12-01
Numerical Methods For Unconstrained Optimization And Nonlinear Equations written by J. E. Dennis, Jr. and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-12-01 with Mathematics categories.
A complete, state-of-the-art description of the methods for unconstrained optimization and systems of nonlinear equations.
Nonlinear Conjugate Gradient Methods For Unconstrained Optimization
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Author : Neculai Andrei
language : en
Publisher: Springer Nature
Release Date : 2020-06-23
Nonlinear Conjugate Gradient Methods For Unconstrained Optimization written by Neculai Andrei and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-23 with Mathematics categories.
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.
A Derivative Free Two Level Random Search Method For Unconstrained Optimization
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Author : Neculai Andrei
language : en
Publisher: Springer Nature
Release Date : 2021-03-31
A Derivative Free Two Level Random Search Method For Unconstrained Optimization written by Neculai Andrei and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-31 with Mathematics categories.
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.
Numerical Methods For Unconstrained Optimization And Nonlinear Equations
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Author : J. E. Dennis
language : en
Publisher: Society for Industrial and Applied Mathematics
Release Date : 1987-01-01
Numerical Methods For Unconstrained Optimization And Nonlinear Equations written by J. E. Dennis and has been published by Society for Industrial and Applied Mathematics this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987-01-01 with Mathematics categories.
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.
Practical Methods Of Optimization Unconstrained Optimization
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Author : Roger Fletcher
language : en
Publisher: John Wiley & Sons
Release Date : 1986
Practical Methods Of Optimization Unconstrained Optimization written by Roger Fletcher and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Mathematics categories.
Methods Of Optimization
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Author : Gordon Raymond Walsh
language : en
Publisher: John Wiley & Sons
Release Date : 1975
Methods Of Optimization written by Gordon Raymond Walsh and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with Mathematics categories.
Nonlinear programming; Search methods for unconstrained optimization; Gradient methods for unconstrained optimziation; Constrained optimization; Dynamic programming.
Unconstrained Optimization And Quantum Calculus
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Author : Bhagwat Ram
language : en
Publisher: Springer Nature
Release Date :
Unconstrained Optimization And Quantum Calculus written by Bhagwat Ram and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Iterative Methods For Optimization
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Author : C. T. Kelley
language : en
Publisher: SIAM
Release Date : 1999-01-01
Iterative Methods For Optimization written by C. T. Kelley and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-01-01 with Mathematics categories.
a carefully selected group of methods for unconstrained and bound constrained optimization problems is analyzed in depth both theoretically and algorithmically. The book focuses on clarity in algorithmic description and analysis rather than generality, and also provides pointers to the literature for the most general theoretical results and robust software,