A Derivative Free Two Level Random Search Method For Unconstrained Optimization

Author : Neculai Andrei
Publisher : Springer Nature
Page : 126 pages
File Size : 52,9 Mb
Release : 2021-03-31
Category : Mathematics
ISBN : 9783030685171

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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 : Neculai Andrei
Publisher : Springer Nature
Page : 824 pages
File Size : 45,8 Mb
Release : 2022-10-18
Category : Mathematics
ISBN : 9783031087202

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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 : Luigi Grippo,Marco Sciandrone
Publisher : Springer Nature
Page : 721 pages
File Size : 47,7 Mb
Release : 2023-05-27
Category : Mathematics
ISBN : 9783031267901

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Introduction to Methods for Nonlinear Optimization by Luigi Grippo,Marco Sciandrone Pdf

This book has two main objectives: • to provide a concise introduction to nonlinear optimization methods, which can be used as a textbook at a graduate or upper undergraduate level; • to collect and organize selected important topics on optimization algorithms, not easily found in textbooks, which can provide material for advanced courses or can serve as a reference text for self-study and research. The basic material on unconstrained and constrained optimization is organized into two blocks of chapters: • basic theory and optimality conditions • unconstrained and constrained algorithms. These topics are treated in short chapters that contain the most important results in theory and algorithms, in a way that, in the authors’ experience, is suitable for introductory courses. A third block of chapters addresses methods that are of increasing interest for solving difficult optimization problems. Difficulty can be typically due to the high nonlinearity of the objective function, ill-conditioning of the Hessian matrix, lack of information on first-order derivatives, the need to solve large-scale problems. In the book various key subjects are addressed, including: exact penalty functions and exact augmented Lagrangian functions, non monotone methods, decomposition algorithms, derivative free methods for nonlinear equations and optimization problems. The appendices at the end of the book offer a review of the essential mathematical background, including an introduction to convex analysis that can make part of an introductory course.

Author : Jorge Nocedal,Stephen Wright
Publisher : Springer Science & Business Media
Page : 636 pages
File Size : 52,9 Mb
Release : 2006-06-06
Category : Mathematics
ISBN : 9780387227429

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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 : Andrew R. Conn,Katya Scheinberg,Luis N. Vicente
Publisher : SIAM
Page : 276 pages
File Size : 43,8 Mb
Release : 2009-04-16
Category : Mathematics
ISBN : 9780898716689

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Introduction to Derivative-Free Optimization by Andrew R. Conn,Katya Scheinberg,Luis N. Vicente Pdf

The first contemporary comprehensive treatment of optimization without derivatives. This text explains how sampling and model techniques are used in derivative-free methods and how they are designed to solve optimization problems. It is designed to be readily accessible to both researchers and those with a modest background in computational mathematics.

Author : Shashi Kant Mishra,Bhagwat Ram
Publisher : Springer Nature
Page : 309 pages
File Size : 50,7 Mb
Release : 2019-12-17
Category : Mathematics
ISBN : 9789811508943

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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 : Charles Audet,Warren Hare
Publisher : Springer
Page : 302 pages
File Size : 42,5 Mb
Release : 2017-12-02
Category : Mathematics
ISBN : 9783319689135

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Derivative-Free and Blackbox Optimization by Charles Audet,Warren Hare Pdf

This book is designed as a textbook, suitable for self-learning or for teaching an upper-year university course on derivative-free and blackbox optimization. The book is split into 5 parts and is designed to be modular; any individual part depends only on the material in Part I. Part I of the book discusses what is meant by Derivative-Free and Blackbox Optimization, provides background material, and early basics while Part II focuses on heuristic methods (Genetic Algorithms and Nelder-Mead). Part III presents direct search methods (Generalized Pattern Search and Mesh Adaptive Direct Search) and Part IV focuses on model-based methods (Simplex Gradient and Trust Region). Part V discusses dealing with constraints, using surrogates, and bi-objective optimization. End of chapter exercises are included throughout as well as 15 end of chapter projects and over 40 figures. Benchmarking techniques are also presented in the appendix.

Author : Neculai Andrei
Publisher : Springer Nature
Page : 515 pages
File Size : 46,9 Mb
Release : 2020-06-23
Category : Mathematics
ISBN : 9783030429508

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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 : Janusz S. Kowalik,Michael Robert Osborne
Publisher : Elsevier Publishing Company
Page : 164 pages
File Size : 41,5 Mb
Release : 1968
Category : Mathematics
ISBN : UOM:39015017334635

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Methods for Unconstrained Optimization Problems by Janusz S. Kowalik,Michael Robert Osborne Pdf

Author : P. Adby
Publisher : Springer Science & Business Media
Page : 214 pages
File Size : 52,7 Mb
Release : 2013-03-09
Category : Science
ISBN : 9789400957053

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Introduction to Optimization Methods by P. Adby Pdf

During the last decade the techniques of non-linear optim ization have emerged as an important subject for study and research. The increasingly widespread application of optim ization has been stimulated by the availability of digital computers, and the necessity of using them in the investigation of large systems. This book is an introduction to non-linear methods of optimization and is suitable for undergraduate and post graduate courses in mathematics, the physical and social sciences, and engineering. The first half of the book covers the basic optimization techniques including linear search methods, steepest descent, least squares, and the Newton-Raphson method. These are described in detail, with worked numerical examples, since they form the basis from which advanced methods are derived. Since 1965 advanced methods of unconstrained and constrained optimization have been developed to utilise the computational power of the digital computer. The second half of the book describes fully important algorithms in current use such as variable metric methods for unconstrained problems and penalty function methods for constrained problems. Recent work, much of which has not yet been widely applied, is reviewed and compared with currently popular techniques under a few generic main headings. vi PREFACE Chapter I describes the optimization problem in mathemat ical form and defines the terminology used in the remainder of the book. Chapter 2 is concerned with single variable optimization. The main algorithms of both search and approximation methods are developed in detail since they are an essential part of many multi-variable methods.

Author : Roger Fletcher
Publisher : John Wiley & Sons
Page : 136 pages
File Size : 42,9 Mb
Release : 1986
Category : Mathematics
ISBN : UOM:39015010639105

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Practical Methods of Optimization: Unconstrained optimization by Roger Fletcher Pdf

Author : C. T. Kelley
Publisher : SIAM
Page : 171 pages
File Size : 43,6 Mb
Release : 2011-09-29
Category : Mathematics
ISBN : 9781611971897

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Implicit Filtering by C. T. Kelley Pdf

A description of the implicit filtering algorithm, its convergence theory and a new MATLAB® implementation.

Author : Bhagwat Ram
Publisher : Springer Nature
Page : 150 pages
File Size : 50,9 Mb
Release : 2024-06-09
Category : Electronic
ISBN : 9789819724352

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Unconstrained Optimization and Quantum Calculus by Bhagwat Ram Pdf

Author : J. E. Dennis, Jr.,Robert B. Schnabel
Publisher : SIAM
Page : 390 pages
File Size : 46,5 Mb
Release : 1996-12-01
Category : Mathematics
ISBN : 9780898713640

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Numerical Methods for Unconstrained Optimization and Nonlinear Equations by J. E. Dennis, Jr.,Robert B. Schnabel Pdf

A complete, state-of-the-art description of the methods for unconstrained optimization and systems of nonlinear equations.

Author : Michael Anthony Wolfe
Publisher : Unknown
Page : 330 pages
File Size : 40,6 Mb
Release : 1978
Category : Mathematics
ISBN : STANFORD:36105031411676

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Numerical Methods for Unconstrained Optimization by Michael Anthony Wolfe Pdf