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 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 Linear and Nonlinear Optimization written by Richard W. Cottle and published by Springer. This book was released on 2017-06-11 with total page 644 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook on Linear and Nonlinear Optimization is intended for graduate and advanced undergraduate students in operations research and related fields. It is both literate and mathematically strong, yet requires no prior course in optimization. As suggested by its title, the book is divided into two parts covering in their individual chapters LP Models and Applications; Linear Equations and Inequalities; The Simplex Algorithm; Simplex Algorithm Continued; Duality and the Dual Simplex Algorithm; Postoptimality Analyses; Computational Considerations; Nonlinear (NLP) Models and Applications; Unconstrained Optimization; Descent Methods; Optimality Conditions; Problems with Linear Constraints; Problems with Nonlinear Constraints; Interior-Point Methods; and an Appendix covering Mathematical Concepts. Each chapter ends with a set of exercises. The book is based on lecture notes the authors have used in numerous optimization courses the authors have taught at Stanford University. It emphasizes modeling and numerical algorithms for optimization with continuous (not integer) variables. The discussion presents the underlying theory without always focusing on formal mathematical proofs (which can be found in cited references). Another feature of this book is its inclusion of cultural and historical matters, most often appearing among the footnotes. "This book is a real gem. The authors do a masterful job of rigorously presenting all of the relevant theory clearly and concisely while managing to avoid unnecessary tedious mathematical details. This is an ideal book for teaching a one or two semester masters-level course in optimization – it broadly covers linear and nonlinear programming effectively balancing modeling, algorithmic theory, computation, implementation, illuminating historical facts, and numerous interesting examples and exercises. Due to the clarity of the exposition, this book also serves as a valuable reference for self-study." Professor Ilan Adler, IEOR Department, UC Berkeley "A carefully crafted introduction to the main elements and applications of mathematical optimization. This volume presents the essential concepts of linear and nonlinear programming in an accessible format filled with anecdotes, examples, and exercises that bring the topic to life. The authors plumb their decades of experience in optimization to provide an enriching layer of historical context. Suitable for advanced undergraduates and masters students in management science, operations research, and related fields." Michael P. Friedlander, IBM Professor of Computer Science, Professor of Mathematics, University of British Columbia
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 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 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 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 Advances in Nonlinear Programming written by Ya-xiang Yuan and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: About 60 scientists and students attended the 96' International Conference on Nonlinear Programming, which was held September 2-5 at Institute of Compu tational Mathematics and Scientific/Engineering Computing (ICMSEC), Chi nese Academy of Sciences, Beijing, China. 25 participants were from outside China and 35 from China. The conference was to celebrate the 60's birthday of Professor M.J.D. Powell (Fellow of Royal Society, University of Cambridge) for his many contributions to nonlinear optimization. On behalf of the Chinese Academy of Sciences, vice president Professor Zhi hong Xu attended the opening ceremony of the conference to express his warm welcome to all the participants. After the opening ceremony, Professor M.J.D. Powell gave the keynote lecture "The use of band matrices for second derivative approximations in trust region methods". 13 other invited lectures on recent advances of nonlinear programming were given during the four day meeting: "Primal-dual methods for nonconvex optimization" by M. H. Wright (SIAM President, Bell Labs), "Interior point trajectories in semidefinite programming" by D. Goldfarb (Columbia University, Editor-in-Chief for Series A of Mathe matical Programming), "An approach to derivative free optimization" by A.
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 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 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 Nonlinear Programming written by Olvi L. Mangasarian and published by SIAM. This book was released on 1994-01-01 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: This reprint of the 1969 book of the same name is a concise, rigorous, yet accessible, account of the fundamentals of constrained optimization theory. Many problems arising in diverse fields such as machine learning, medicine, chemical engineering, structural design, and airline scheduling can be reduced to a constrained optimization problem. This book provides readers with the fundamentals needed to study and solve such problems. Beginning with a chapter on linear inequalities and theorems of the alternative, basics of convex sets and separation theorems are then derived based on these theorems. This is followed by a chapter on convex functions that includes theorems of the alternative for such functions. These results are used in obtaining the saddlepoint optimality conditions of nonlinear programming without differentiability assumptions.
Download or read book Least Squares Viewed as a General Optimization Problem written by Robert Patrick Kelley and published by . This book was released on 1977 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: Least squares problems arise when one attempts to fit a model y = n(x, beta) to points (y1,x1), ..., (yn, xn). Solutions to such problems are obtained by optimizing the sum of squared deviations over an admissible region. This paper discusses the basic theory of optimization for a general objective function and applies this material to both the linear and nonlinear least squares problems. In linear least squares normal equations for both the full rank and less than full rank cases are considered and the Kuhn-Tucker conditions are used to obtain the normal equations under linear inequality constraints. In nonlinear least squares, different iterative procedures, which may be used to obtain a solution, are discussed. The methods considered are steepest descent, Newton-Raphson, Gauss-Newton, Hartley's modified Gauss-Newton, and that of Marquardt. Results are obtained which relate Marquardt's method to equality constrained least squares. (Author).
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 Nonlinear Programming written by Anthony V. Fiacco and published by SIAM. This book was released on 1990-01-01 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent interest in interior point methods generated by Karmarkar's Projective Scaling Algorithm has created a new demand for this book because the methods that have followed from Karmarkar's bear a close resemblance to those described. There is no other source for the theoretical background of the logarithmic barrier function and other classical penalty functions. Analyzes in detail the "central" or "dual" trajectory used by modern path following and primal/dual methods for convex and general linear programming. As researchers begin to extend these methods to convex and general nonlinear programming problems, this book will become indispensable to them.
