Download or read book A Contribution to Theory and Practice of Nonlinear Parameter Optimization written by Ph. Th Stol and published by . This book was released on 1975 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear parameter optimization in least squares was studied from a point of view of differential geometry. Properties of curvilinear coordinates, scale factors and curvature were investigated. Parameters of the condition function were expressed as functions of algorithm parameters to generalize the formulas. The analysis of the convergence process cumulated in the development of procedures that accelerate convergence. Scale factors were used as weights to the differential correction vector to improve the direction of search. A method to correct for curvature, called back projection method, was developed. Use was made of the tangent plane on which the path of search on the fitting surface was projected. Deviations from the original direction were corrected by optimizing the angle of deviation and the step factor. The correspondence between rate of convergence and curvature of the path of search was illustrated with an example. A small geodesic curvature at the starting point indicates fast convergence. Curvature properties of the parametric curves appeared to be of more influence than those of the fitting surface. To avoid heavy oscillation of intermediate parameter values a method was developed that required the intermediate points to be the foot of a perpendicular from the terminal point of intermediate observation vectors thus producing paths of controlled approach. Since condition functions may have a complicated structure in that they can be implicit functions, sequential functions or can consist of mathematical models involving alternative functions, it was treated how first derivatives can be calculated and programmed systematically for these functions. Methods introduced were made operational by means of a FORTRAN program. A description of the use of the subprograms and instructions to modify the main program to suit the various algorithms and procedures developed are given in the Appendices.
Download or read book A Contribution to Theory and Practice of Nonlinear Parameter Optimization written by Philip Thomas Stol and published by . This book was released on 1975 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A contribution to theory and pratice of nonlinear parameter optimization written by P.T. Stol and published by . This book was released on 1975 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Optimization Theory and Practice written by Wilhelm Forst and published by Springer Science & Business Media. This book was released on 2010-07-26 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization is a field important in its own right but is also integral to numerous applied sciences, including operations research, management science, economics, finance and all branches of mathematics-oriented engineering. Constrained optimization models are one of the most widely used mathematical models in operations research and management science. This book gives a modern and well-balanced presentation of the subject, focusing on theory but also including algorithims and examples from various real-world applications. Detailed examples and counter-examples are provided--as are exercises, solutions and helpful hints, and Matlab/Maple supplements.
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.
Download or read book An Introduction to Nonlinear Optimization Theory written by Marius Durea and published by Walter de Gruyter GmbH & Co KG. This book was released on 2014-01-01 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this book is to present the main ideas and techniques in the field of continuous smooth and nonsmooth optimization. Starting with the case of differentiable data and the classical results on constrained optimization problems, and continuing with the topic of nonsmooth objects involved in optimization theory, the book concentrates on both theoretical and practical aspects of this field. This book prepares those who are engaged in research by giving repeated insights into ideas that are subsequently dealt with and illustrated in detail.
Download or read book Nonlinear Optimization in Finite Dimensions written by Hubertus Th. Jongen and published by Springer Science & Business Media. This book was released on 2013-12-11 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: At the heart of the topology of global optimization lies Morse Theory: The study of the behaviour of lower level sets of functions as the level varies. Roughly speaking, the topology of lower level sets only may change when passing a level which corresponds to a stationary point (or Karush-Kuhn Tucker point). We study elements of Morse Theory, both in the unconstrained and constrained case. Special attention is paid to the degree of differentiabil ity of the functions under consideration. The reader will become motivated to discuss the possible shapes and forms of functions that may possibly arise within a given problem framework. In a separate chapter we show how certain ideas may be carried over to nonsmooth items, such as problems of Chebyshev approximation type. We made this choice in order to show that a good under standing of regular smooth problems may lead to a straightforward treatment of "just" continuous problems by means of suitable perturbation techniques, taking a priori nonsmoothness into account. Moreover, we make a focal point analysis in order to emphasize the difference between inner product norms and, for example, the maximum norm. Then, specific tools from algebraic topol ogy, in particular homology theory, are treated in some detail. However, this development is carried out only as far as it is needed to understand the relation between critical points of a function on a manifold with structured boundary. Then, we pay attention to three important subjects in nonlinear optimization.
Download or read book Introduction to the Theory of Nonlinear Optimization written by Johannes Jahn and published by Springer Nature. This book was released on 2020-07-02 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book serves as an introductory text to optimization theory in normed spaces and covers all areas of nonlinear optimization. It presents fundamentals with particular emphasis on the application to problems in the calculus of variations, approximation and optimal control theory. The reader is expected to have a basic knowledge of linear functional analysis.
Download or read book Optimization written by Mohan C. Joshi and published by Alpha Science Int'l Ltd.. This book was released on 2004 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gives a detailed mathematical exposition to various optimization techniques. This book includes topics such as: Single and multi-dimensional optimization, Linear programming, Nonlinear constrained optimization and Evolutionary algorithms.
Download or read book Journal of Statistical Research written by and published by . This book was released on 1976 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nonlinear Optimization and Applications written by Gianni Pillo and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the edited texts of the lectures presented at the workshop on Nonlinear Optimization: Theory and Applications, held in Erice at the "G. Stampacchia" School of Mathematics of the "E. Majorana" International Centre for Scientific Culture June 13-21, 1995. The meeting was conceived to review and discuss recent advances and promising research trends concerning theory, algorithms, and innovative applications in the field This is a field of mathematics which is providing viable of Nonlinear Optimization. tools in engineering, in economics and in other applied sciences, and which is giving a great contribution also in the solution of the more practiced linear optimization prob lems. The meeting was attended by approximately 70 people from 18 countries. Besides the lectures, several formal and informal discussions took place. The result was a broad exposure providing a wide and deep understanding of the present research achievements in the field. We wish to express our appreciation for the active contributions of all the partici pants in the meeting. Our gratitude is due to the Ettore Majorana Center in Erice, which offered its facilities and stimulating environment: its staff was certainly instrumental for the success of the meeting. Our gratitude is also due to Francisco Facchinei and Massino Roma for the time spent in the organization of the workshop, and to Giuliana Cai for the careful typesetting of this volume.
Download or read book Practical Methods of Optimization written by R. Fletcher and published by John Wiley & Sons. This book was released on 2000-07-26 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Introduction to Nonlinear Optimization written by Amir Beck and published by SIAM. This book was released on 2014-10-27 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the foundations of the theory of nonlinear optimization as well as some related algorithms and presents a variety of applications from diverse areas of applied sciences. The author combines three pillars of optimization?theoretical and algorithmic foundation, familiarity with various applications, and the ability to apply the theory and algorithms on actual problems?and rigorously and gradually builds the connection between theory, algorithms, applications, and implementation. Readers will find more than 170 theoretical, algorithmic, and numerical exercises that deepen and enhance the reader's understanding of the topics. The author includes offers several subjects not typically found in optimization books?for example, optimality conditions in sparsity-constrained optimization, hidden convexity, and total least squares. The book also offers a large number of applications discussed theoretically and algorithmically, such as circle fitting, Chebyshev center, the Fermat?Weber problem, denoising, clustering, total least squares, and orthogonal regression and theoretical and algorithmic topics demonstrated by the MATLAB? toolbox CVX and a package of m-files that is posted on the book?s web site.
Download or read book American Scientist written by and published by . This book was released on 1942 with total page 780 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Non linear Predictive Control written by Basil Kouvaritakis and published by IET. This book was released on 2001-10-26 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: The advantage of model predictive control is that it can take systematic account of constraints, thereby allowing processes to operate at the limits of achievable performance. Engineers in academia, industry, and government from the US and Europe explain how the linear version can be adapted and applied to the nonlinear conditions that characterize the dynamics of most real manufacturing plants. They survey theoretical and practical trends, describe some specific theories and demonstrate their practical application, derive strategies that provide appropriate assurance of closed-loop stability, and discuss practical implementation. Annotation copyrighted by Book News, Inc., Portland, OR
Download or read book Introduction to Nonlinear Optimization written by Amir Beck and published by SIAM. This book was released on 2023-06-29 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: Built on the framework of the successful first edition, this book serves as a modern introduction to the field of optimization. The author’s objective is to provide the foundations of theory and algorithms of nonlinear optimization as well as to present a variety of applications from diverse areas of applied sciences. Introduction to Nonlinear Optimization gradually yet rigorously builds connections between theory, algorithms, applications, and actual implementation. The book contains several topics not typically included in optimization books, such as optimality conditions in sparsity constrained optimization, hidden convexity, and total least squares. Readers will discover a wide array of applications such as circle fitting, Chebyshev center, the Fermat–Weber problem, denoising, clustering, total least squares, and orthogonal regression. These applications are studied both theoretically and algorithmically, illustrating concepts such as duality. Python and MATLAB programs are used to show how the theory can be implemented. The extremely popular CVX toolbox (MATLAB) and CVXPY module (Python) are described and used. More than 250 theoretical, algorithmic, and numerical exercises enhance the reader's understanding of the topics. (More than 70 of the exercises provide detailed solutions, and many others are provided with final answers.) The theoretical and algorithmic topics are illustrated by Python and MATLAB examples. This book is intended for graduate or advanced undergraduate students in mathematics, computer science, electrical engineering, and potentially other engineering disciplines.
Download or read book Numerical Methods for Unconstrained Optimization and Nonlinear Equations written by J. E. Dennis, Jr. and published by SIAM. This book was released on 1996-12-01 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. The level of presentation is consistent throughout, with a good mix of examples and theory, making it a valuable text at both the graduate and undergraduate level. It has been praised as excellent for courses with approximately the same name as the book title and would also be useful as a supplemental text for a nonlinear programming or a numerical analysis course. Many exercises are provided to illustrate and develop the ideas in the text. A large appendix provides a mechanism for class projects and a reference for readers who want the details of the algorithms. Practitioners may use this book for self-study and reference. For complete understanding, readers should have a background in calculus and linear algebra. The book does contain background material in multivariable calculus and numerical linear algebra.
