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Conjugate Gradient Algorithms In Nonconvex Optimization
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Book Synopsis Conjugate Gradient Algorithms in Nonconvex Optimization by : Radoslaw Pytlak
Download or read book Conjugate Gradient Algorithms in Nonconvex Optimization written by Radoslaw Pytlak and published by Springer Science & Business Media. This book was released on 2008-11-18 with total page 493 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Conjugate Gradient Algorithms and Finite Element Methods by : Michal Krizek
Download or read book Conjugate Gradient Algorithms and Finite Element Methods written by Michal Krizek and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: The position taken in this collection of pedagogically written essays is that conjugate gradient algorithms and finite element methods complement each other extremely well. Via their combinations practitioners have been able to solve complicated, direct and inverse, multidemensional problems modeled by ordinary or partial differential equations and inequalities, not necessarily linear, optimal control and optimal design being part of these problems. The aim of this book is to present both methods in the context of complicated problems modeled by linear and nonlinear partial differential equations, to provide an in-depth discussion on their implementation aspects. The authors show that conjugate gradient methods and finite element methods apply to the solution of real-life problems. They address graduate students as well as experts in scientific computing.
Book Synopsis Nonlinear Conjugate Gradient Methods for Unconstrained Optimization by : Neculai Andrei
Download or read book Nonlinear Conjugate Gradient Methods for Unconstrained Optimization written by Neculai Andrei and published by Springer Nature. This book was released on 2020-06-23 with total page 515 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Nonlinear Conjugate Gradient Methods for Unconstrained Optimization by : Neculai Andrei
Download or read book Nonlinear Conjugate Gradient Methods for Unconstrained Optimization written by Neculai Andrei and published by Springer. This book was released on 2020-06-29 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Fitting Linear Models by : A. McIntosh
Download or read book Fitting Linear Models written by A. McIntosh and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: The increasing power and decreasing price of smalI computers, especialIy "personal" computers, has made them increasingly popular in statistical analysis. The day may not be too far off when every statistician has on his or her desktop computing power on a par with the large mainframe computers of 15 or 20 years ago. These same factors make it relatively easy to acquire and manipulate large quantities of data, and statisticians can expect a corresponding increase in the size of the datasets that they must analyze. Unfortunately, because of constraints imposed by architecture, size or price, these smalI computers do not possess the main memory of their large cousins. Thus, there is a growing need for algorithms that are sufficiently economical of space to permit statistical analysis on smalI computers. One area of analysis where there is a need for algorithms that are economical of space is in the fitting of linear models.
Book Synopsis Evaluation Complexity of Algorithms for Nonconvex Optimization by : Coralia Cartis
Download or read book Evaluation Complexity of Algorithms for Nonconvex Optimization written by Coralia Cartis and published by SIAM. This book was released on 2022-07-06 with total page 549 pages. Available in PDF, EPUB and Kindle. Book excerpt: A popular way to assess the “effort” needed to solve a problem is to count how many evaluations of the problem functions (and their derivatives) are required. In many cases, this is often the dominating computational cost. Given an optimization problem satisfying reasonable assumptions—and given access to problem-function values and derivatives of various degrees—how many evaluations might be required to approximately solve the problem? Evaluation Complexity of Algorithms for Nonconvex Optimization: Theory, Computation, and Perspectives addresses this question for nonconvex optimization problems, those that may have local minimizers and appear most often in practice. This is the first book on complexity to cover topics such as composite and constrained optimization, derivative-free optimization, subproblem solution, and optimal (lower and sharpness) bounds for nonconvex problems. It is also the first to address the disadvantages of traditional optimality measures and propose useful surrogates leading to algorithms that compute approximate high-order critical points, and to compare traditional and new methods, highlighting the advantages of the latter from a complexity point of view. This is the go-to book for those interested in solving nonconvex optimization problems. It is suitable for advanced undergraduate and graduate students in courses on advanced numerical analysis, data science, numerical optimization, and approximation theory.
Book Synopsis Unconstrained Optimization and Quantum Calculus by : Bhagwat Ram
Download or read book Unconstrained Optimization and Quantum Calculus written by Bhagwat Ram and published by Springer Nature. This book was released on with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Integer and Nonlinear Programming by : Philip Wolfe
Download or read book Integer and Nonlinear Programming written by Philip Wolfe and published by . This book was released on 1970 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: A NATO Summer School held in Bandol, France, sponsored by the Scientific Affairs Division of NATO.
Book Synopsis The Lanczos and Conjugate Gradient Algorithms by : Gerard Meurant
Download or read book The Lanczos and Conjugate Gradient Algorithms written by Gerard Meurant and published by SIAM. This book was released on 2006-01-01 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Lanczos and conjugate gradient (CG) algorithms are fascinating numerical algorithms. This book presents the most comprehensive discussion to date of the use of these methods for computing eigenvalues and solving linear systems in both exact and floating point arithmetic. The author synthesizes the research done over the past 30 years, describing and explaining the "average" behavior of these methods and providing new insight into their properties in finite precision. Many examples are given that show significant results obtained by researchers in the field. The author emphasizes how both algorithms can be used efficiently in finite precision arithmetic, regardless of the growth of rounding errors that occurs. He details the mathematical properties of both algorithms and demonstrates how the CG algorithm is derived from the Lanczos algorithm. Loss of orthogonality involved with using the Lanczos algorithm, ways to improve the maximum attainable accuracy of CG computations, and what modifications need to be made when the CG method is used with a preconditioner are addressed.
Book Synopsis Handbook Of Machine Learning - Volume 2: Optimization And Decision Making by : Tshilidzi Marwala
Download or read book Handbook Of Machine Learning - Volume 2: Optimization And Decision Making written by Tshilidzi Marwala and published by World Scientific. This book was released on 2019-11-21 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: Building on , this volume on Optimization and Decision Making covers a range of algorithms and their applications. Like the first volume, it provides a starting point for machine learning enthusiasts as a comprehensive guide on classical optimization methods. It also provides an in-depth overview on how artificial intelligence can be used to define, disprove or validate economic modeling and decision making concepts.
Book Synopsis Fundamentals of Deep Learning by : Nikhil Buduma
Download or read book Fundamentals of Deep Learning written by Nikhil Buduma and published by "O'Reilly Media, Inc.". This book was released on 2017-05-25 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: With the reinvigoration of neural networks in the 2000s, deep learning has become an extremely active area of research, one that’s paving the way for modern machine learning. In this practical book, author Nikhil Buduma provides examples and clear explanations to guide you through major concepts of this complicated field. Companies such as Google, Microsoft, and Facebook are actively growing in-house deep-learning teams. For the rest of us, however, deep learning is still a pretty complex and difficult subject to grasp. If you’re familiar with Python, and have a background in calculus, along with a basic understanding of machine learning, this book will get you started. Examine the foundations of machine learning and neural networks Learn how to train feed-forward neural networks Use TensorFlow to implement your first neural network Manage problems that arise as you begin to make networks deeper Build neural networks that analyze complex images Perform effective dimensionality reduction using autoencoders Dive deep into sequence analysis to examine language Learn the fundamentals of reinforcement learning
Book Synopsis Proximal Algorithms by : Neal Parikh
Download or read book Proximal Algorithms written by Neal Parikh and published by Now Pub. This book was released on 2013-11 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proximal Algorithms discusses proximal operators and proximal algorithms, and illustrates their applicability to standard and distributed convex optimization in general and many applications of recent interest in particular. Much like Newton's method is a standard tool for solving unconstrained smooth optimization problems of modest size, proximal algorithms can be viewed as an analogous tool for nonsmooth, constrained, large-scale, or distributed versions of these problems. They are very generally applicable, but are especially well-suited to problems of substantial recent interest involving large or high-dimensional datasets. Proximal methods sit at a higher level of abstraction than classical algorithms like Newton's method: the base operation is evaluating the proximal operator of a function, which itself involves solving a small convex optimization problem. These subproblems, which generalize the problem of projecting a point onto a convex set, often admit closed-form solutions or can be solved very quickly with standard or simple specialized methods. Proximal Algorithms discusses different interpretations of proximal operators and algorithms, looks at their connections to many other topics in optimization and applied mathematics, surveys some popular algorithms, and provides a large number of examples of proximal operators that commonly arise in practice.
Book Synopsis System Modeling and Optimization by : F. Ceragioli
Download or read book System Modeling and Optimization written by F. Ceragioli and published by Springer. This book was released on 2006-06-07 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents selected proceedings from the 22nd biennial IFIP conference on System Modeling and Optimization, held in Turin, Italy in July of 2005. This edition of the conference is dedicated to the achievements of Camillo Possio, who was killed sixty years ago during the last air raid over Turin. For more information about the 300 other books in the IFIP series, please visit www.springeronline.com.
Book Synopsis High Performance Algorithms and Software for Nonlinear Optimization by : Gianni Pillo
Download or read book High Performance Algorithms and Software for Nonlinear Optimization written by Gianni Pillo and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the edited texts of the lectures presented at the Workshop on High Performance Algorithms and Software for Nonlinear Optimization held in Erice, Sicily, at the "G. Stampacchia" School of Mathematics of the "E. Majorana" Centre for Scientific Culture, June 30 - July 8, 2001. In the first year of the new century, the aim of the Workshop was to assess the past and to discuss the future of Nonlinear Optimization, and to highlight recent achieve ments and promising research trends in this field. An emphasis was requested on algorithmic and high performance software developments and on new computational experiences, as well as on theoretical advances. We believe that such goal was basically achieved. The Workshop was attended by 71 people from 22 countries. Although not all topics were covered, the presentations gave indeed a wide overview of the field, from different and complementary stand points. Besides the lectures, several formal and informal discussions took place. We wish to express our appreciation for the active contribution of all the participants in the meeting. The 18 papers included in this volume represent a significant selection of the most recent developments in nonlinear programming theory and practice. They show that there is plenty of exciting ideas, implementation issues and new applications which produce a very fast evolution in the field.
Book Synopsis Engineering Mathematics and Artificial Intelligence by : Herb Kunze
Download or read book Engineering Mathematics and Artificial Intelligence written by Herb Kunze and published by CRC Press. This book was released on 2023-07-26 with total page 717 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fields of Artificial Intelligence (AI) and Machine Learning (ML) have grown dramatically in recent years, with an increasingly impressive spectrum of successful applications. This book represents a key reference for anybody interested in the intersection between mathematics and AI/ML and provides an overview of the current research streams. Engineering Mathematics and Artificial Intelligence: Foundations, Methods, and Applications discusses the theory behind ML and shows how mathematics can be used in AI. The book illustrates how to improve existing algorithms by using advanced mathematics and offers cutting-edge AI technologies. The book goes on to discuss how ML can support mathematical modeling and how to simulate data by using artificial neural networks. Future integration between ML and complex mathematical techniques is also highlighted within the book. This book is written for researchers, practitioners, engineers, and AI consultants.
Author :Prateek Jain Publisher :Foundations and Trends in Machine Learning ISBN 13 :9781680833683 Total Pages :218 pages Book Rating :4.8/5 (336 download)
Book Synopsis Non-convex Optimization for Machine Learning by : Prateek Jain
Download or read book Non-convex Optimization for Machine Learning written by Prateek Jain and published by Foundations and Trends in Machine Learning. This book was released on 2017-12-04 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: Non-convex Optimization for Machine Learning takes an in-depth look at the basics of non-convex optimization with applications to machine learning. It introduces the rich literature in this area, as well as equips the reader with the tools and techniques needed to apply and analyze simple but powerful procedures for non-convex problems. Non-convex Optimization for Machine Learning is as self-contained as possible while not losing focus of the main topic of non-convex optimization techniques. The monograph initiates the discussion with entire chapters devoted to presenting a tutorial-like treatment of basic concepts in convex analysis and optimization, as well as their non-convex counterparts. The monograph concludes with a look at four interesting applications in the areas of machine learning and signal processing, and exploring how the non-convex optimization techniques introduced earlier can be used to solve these problems. The monograph also contains, for each of the topics discussed, exercises and figures designed to engage the reader, as well as extensive bibliographic notes pointing towards classical works and recent advances. Non-convex Optimization for Machine Learning can be used for a semester-length course on the basics of non-convex optimization with applications to machine learning. On the other hand, it is also possible to cherry pick individual portions, such the chapter on sparse recovery, or the EM algorithm, for inclusion in a broader course. Several courses such as those in machine learning, optimization, and signal processing may benefit from the inclusion of such topics.
Book Synopsis Global Optimization with Non-Convex Constraints by : Roman G. Strongin
Download or read book Global Optimization with Non-Convex Constraints written by Roman G. Strongin and published by Springer Science & Business Media. This book was released on 2013-11-09 with total page 717 pages. Available in PDF, EPUB and Kindle. Book excerpt: Everything should be made as simple as possible, but not simpler. (Albert Einstein, Readers Digest, 1977) The modern practice of creating technical systems and technological processes of high effi.ciency besides the employment of new principles, new materials, new physical effects and other new solutions ( which is very traditional and plays the key role in the selection of the general structure of the object to be designed) also includes the choice of the best combination for the set of parameters (geometrical sizes, electrical and strength characteristics, etc.) concretizing this general structure, because the Variation of these parameters ( with the structure or linkage being already set defined) can essentially affect the objective performance indexes. The mathematical tools for choosing these best combinations are exactly what is this book about. With the advent of computers and the computer-aided design the pro bations of the selected variants are usually performed not for the real examples ( this may require some very expensive building of sample op tions and of the special installations to test them ), but by the analysis of the corresponding mathematical models. The sophistication of the mathematical models for the objects to be designed, which is the natu ral consequence of the raising complexity of these objects, greatly com plicates the objective performance analysis. Today, the main (and very often the only) available instrument for such an analysis is computer aided simulation of an object's behavior, based on numerical experiments with its mathematical model.
