Download or read book Generally Constrained Nonlinear Least Squares and Generating Nonlinear Programming Test Problems written by Nezameddin Mahdavi-Amiri and published by . This book was released on 1984 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book More Test Examples for Nonlinear Programming Codes written by Klaus Schittkowski and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of 188 nonlinear programming test examples is a supplement of the test problem collection published by Hock and Schittkowski [2]. As in the former case, the intention is to present an extensive set of nonlinear programming problems that were used by other authors in the past to develop, test or compare optimization algorithms. There is no distinction between an "easy" or "difficult" test problem, since any related classification must depend on the underlying algorithm and test design. For instance, a nonlinear least squares problem may be solved easily by a special purpose code within a few iterations, but the same problem can be unsolvable for a general nonlinear programming code due to ill-conditioning. Thus one should consider both collections as a possible offer to choose some suitable problems for a specific test frame. One difference between the new collection and the former one pub lished by Hock and Schittkowski [2], is the attempt to present some more realistic or "real world" problems. Moreover a couple of non linear least squares test problems were collected which can be used e. g. to test data fitting algorithms. The presentation of the test problems is somewhat simplified and numerical solutions are computed only by one nonlinear programming code, the sequential quadratic programming algorithm NLPQL of Schittkowski [3]. But both test problem collections are implemeted in the same way in form of special FORTRAN subroutines, so that the same test programs can be used.
Download or read book Numerical Methods for Least Squares Problems written by Ake Bjorck and published by SIAM. This book was released on 1996-12-01 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: The method of least squares: the principal tool for reducing the influence of errors when fitting models to given observations.
Download or read book Test Problems for Constrained Nonlinear Mathematical Programming Algorithms written by and published by . This book was released on 1978 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The report presents a collection of constrained nonlinear programming problems for use in testing optimization algorithms. The problems vary in size from two variables to one hundred variables with various combinations of linear/nonlinear constraints and objective functions. IBM FORTRAN IV programs were written to provide function values and gradients for the objective function and constraints. Each coded problem was checked at several points against published results, and a validation process was used to check the values of the objective function, constraints, and gradients. The problems were collected from various sources, and many of them have been used by other authors in published results of their algorithm testing. This report should also be useful in an educational setting to provide students with experience in nontrivial problems. Listings of the IBM FORTRAN code are included in this report. 10 tables.
Download or read book CNLLS written by Nezam Mahdavi-Amiri and published by . This book was released on 1987 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A New Algorithm for Constrained Nonlinear Least squares Problems written by Richard J. Hanson and published by . This book was released on 1983 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book American Doctoral Dissertations written by and published by . This book was released on 1981 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Test Examples for Nonlinear Programming Codes written by W. Hock and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: ................................................................. The performance of a nonlinear programming algorithm can only be ascertained by numerical experiments requiring the collection and implementation of test examples in dependence upon the desired performance criterium. This book should be considered as an assis tance for a test designer since it presents an extensive collec tion of nonlinear programming problems which have been used in the past to test or compare optimization programs. He will be in formed about the optimal solution, about the structure of the problem in the neighbourhood of the solution, and, in addition, about the usage of the corresp,onding FORTRAN subroutines if he is interested in obtaining them -ofi a magnetic tape. Chapter I shows how the test examples are documented. In par ticular, the evaluation of computable information about the solu tion of a problem is outlined. It is explained how the optimal solution, the optimal Lagrange-multipliers, and the condition number of the projected Hessian of the Lagrangian are obtained. Furthermore, a classification number is defined allowing a formal description of a test problem, and the documentation scheme is described which is used in Chapter IV to present the problems.
Download or read book Nonlinear Programming written by Mokhtar S. Bazaraa and published by Wiley-Interscience. This book was released on 2006-05-26 with total page 872 pages. Available in PDF, EPUB and Kindle. Book excerpt: COMPREHENSIVE COVERAGE OF NONLINEAR PROGRAMMING THEORY AND ALGORITHMS, THOROUGHLY REVISED AND EXPANDED Nonlinear Programming: Theory and Algorithms—now in an extensively updated Third Edition—addresses the problem of optimizing an objective function in the presence of equality and inequality constraints. Many realistic problems cannot be adequately represented as a linear program owing to the nature of the nonlinearity of the objective function and/or the nonlinearity of any constraints. The Third Edition begins with a general introduction to nonlinear programming with illustrative examples and guidelines for model construction. Concentration on the three major parts of nonlinear programming is provided: Convex analysis with discussion of topological properties of convex sets, separation and support of convex sets, polyhedral sets, extreme points and extreme directions of polyhedral sets, and linear programming Optimality conditions and duality with coverage of the nature, interpretation, and value of the classical Fritz John (FJ) and the Karush-Kuhn-Tucker (KKT) optimality conditions; the interrelationships between various proposed constraint qualifications; and Lagrangian duality and saddle point optimality conditions Algorithms and their convergence, with a presentation of algorithms for solving both unconstrained and constrained nonlinear programming problems Important features of the Third Edition include: New topics such as second interior point methods, nonconvex optimization, nondifferentiable optimization, and more Updated discussion and new applications in each chapter Detailed numerical examples and graphical illustrations Essential coverage of modeling and formulating nonlinear programs Simple numerical problems Advanced theoretical exercises The book is a solid reference for professionals as well as a useful text for students in the fields of operations research, management science, industrial engineering, applied mathematics, and also in engineering disciplines that deal with analytical optimization techniques. The logical and self-contained format uniquely covers nonlinear programming techniques with a great depth of information and an abundance of valuable examples and illustrations that showcase the most current advances in nonlinear problems.
Download or read book Solution of Nonlinear Least squares Problems written by Christina Fraley and published by . This book was released on 1987 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation addresses the nonlinear least-squares problem where f(x) is a vector whose components are smooth nonlinear functions. The problem arises most often in data fitting applications. Much research has focused on the development of specialized algorithms that attempt to exploit the structure of the nonlinear least-squares objective. We assume that n and m are relatively small, so that limited storage and sparsity in the derivatives of f need not be taken into account in formulating algorithms. We first discuss existing numerical algorithms for nonlinear least squares, nearly all of which involve iterative minimization of quadratic function. Methods for general unconstrained optimization, Gauss-Newton methods, Levenberg-Marquardt methods, and special quasi-Newton methods are among the algorithms surveyed. Our emphasis is on those methods that form the basis of widely-distributed software, and numerical results are given for a large set of test problems. The main contribution of this research is to propose new algorithms that make use of more general quadratic programming subproblems. Options are investigated that are based on convergence properties of sequential quadratic programming methods for constrained optimization, and on geometric considerations in nonlinear least squares. Numerical results are given, demonstrating that the new methods may be useful in practice.
Download or read book Comprehensive Dissertation Index written by and published by . This book was released on 1984 with total page 974 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vols. for 1973- include the following subject areas: Biological sciences, Agriculture, Chemistry, Environmental sciences, Health sciences, Engineering, Mathematics and statistics, Earth sciences, Physics, Education, Psychology, Sociology, Anthropology, History, Law & political science, Business & economics, Geography & regional planning, Language & literature, Fine arts, Library & information science, Mass communications, Music, Philosophy and Religion.
Download or read book Handbook of Numerical Analysis written by Philippe G. Ciarlet and published by North-Holland is. This book was released on 1990 with total page 688 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Least Squares Computations in Science and Engineering written by and published by . This book was released on 1994 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: Least squares computations constitute a fundamental tool in science and engineering. The reason is that they play a critical role in fitting numerical models to real world observations. This AFOSR supported research effort has been concerned with the design and testing of new algorithms for least squares computations and optimization in science and engineering. The objectives were to mathematically develop, test, and analyze fast numerical algorithms for the efficient solution to problems on modem high performance computers. The focus of this project was the application of scientific computing technology in the area of signal and image processing. Very many problems lead to over determined systems of linear or nonlinear equations that are often solved by least squares or related optimization methods. Generally, the problems are accompanied by constraints, such as bound constraints, and the observations are corrupted by noise. The project has involved the application of scientific computing in the area of computational linear and nonlinear least squares methods with particular applications in image and signal processing, where recovering images is often an ill-posed inverse problem. Additional work included control computations associated with adaptive optics. Constrained least squares, Adaptive filtering, Adaptive optics, Deconvolution, Image restoration, Parallel algorithms, Trace maximization, Inverse problems, FFT.
Download or read book Notices of the American Mathematical Society written by American Mathematical Society and published by . This book was released on 1982 with total page 720 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Comprehensive Dissertation Index Mathematics Statistics Physics A E written by and published by . This book was released on 1984 with total page 1008 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Algorithms for Nonlinear Least squares Problems written by Stanford University Center for Large Scale Scientific Computation and published by . This book was released on 1988 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "This paper addresses the nonlinear least-squares problem min [formula], where f(x) is a vector in [symbol] whose components are smooth nonlinear functions. The problem arises most often in data fitting applications. Much research has focused on the development of specialized algorithms that attempt to exploit the structure of the nonlinear least-squares objective. We survey numerical methods developed for problems in which sparsity in the derivatives of f is not taken into account in formulationg algorithms."
Download or read book Dissertation Abstracts International written by and published by . This book was released on 1995 with total page 796 pages. Available in PDF, EPUB and Kindle. Book excerpt:
