Numerical Algorithms For Nonlinearly Constrained Optimization
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Numerical Algorithms For Nonlinearly Constrained Optimization
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Author : Michael Thomas Heath
language : en
Publisher:
Release Date : 1978
Numerical Algorithms For Nonlinearly Constrained Optimization written by Michael Thomas Heath and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with Algorithms categories.
This dissertation is concerned with the development and numerical implementation of algorithms for solving finite dimensional optimization problems. Special emphasis is given to robustness, by which is meant the ability of an algorithm to cope with adverse circumstances, whether due to pathologies of a particular problem or to the shortcomings of finite precision computer arithmetic. A uniform framework is developed in which a common set of techniques may be applied to all of the standard problems of optimization. The algorithms are based on Newton-like methods implemented in a robust manner by means of hybrid, curved line searches and stable linear algebra techniques. Developed first in the context of systems of nonlinear equations, nonlinear least squares, and unconstrained minimization, the algorithms are combined and extended to include problems with equality or inequality constraints. Constrained problems are handled by means of separate line searches in the range and null spaces of the matrix of constraint normals. The classical Lagrangian is modified to allow the same Newton-like methods to be applied to inequality constraints. Test results are presented which show the validity and promise of the methods developed in this dissertation. (Author).
Numerical Algorithms For Nonlinearly Constrained Optimization
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Author : Michael Thomas Heath
language : en
Publisher:
Release Date : 1978
Numerical Algorithms For Nonlinearly Constrained Optimization written by Michael Thomas Heath and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with Algorithms categories.
This dissertation is concerned with the development and numerical implementation of algorithms for solving finite dimensional optimization problems. Special emphasis is given to robustness, by which is meant the ability of an algorithm to cope with adverse circumstances, whether due to pathologies of a particular problem or to the shortcomings of finite precision computer arithmetic. A uniform framework is developed in which a common set of techniques may be applied to all of the standard problems of optimization. The algorithms are based on Newton-like methods implemented in a robust manner by means of hybrid, curved line searches and stable linear algebra techniques. Developed first in the context of systems of nonlinear equations, nonlinear least squares, and unconstrained minimization, the algorithms are combined and extended to include problems with equality or inequality constraints. Constrained problems are handled by means of separate line searches in the range and null spaces of the matrix of constraint normals. The classical Lagrangian is modified to allow the same Newton-like methods to be applied to inequality constraints. Test results are presented which show the validity and promise of the methods developed in this dissertation. (Author).
Survey Of Available Software For Nonlinearly Constrained Optimization
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Author : Stanford University. Department of Operations Research. Systems Optimization Laboratory
language : en
Publisher:
Release Date : 1978
Survey Of Available Software For Nonlinearly Constrained Optimization written by Stanford University. Department of Operations Research. Systems Optimization Laboratory and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with categories.
The aim of this paper is to present a brief overview of current practice in solving nonlinearly constrained optimization problems. First, we consider selected theoretical and computational aspects of some of the widely used methods for such problems. Second, the status of implementations of such methods will be sketched. The latter discussion will include: factors to be considered in evaluating optimization programs; guidelines concerning the application of a general-purpose routine to any particular problem; and a list of some available software. (Author).
Algorithms For Nonlinearly Constrained Optimization
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Author : Stanford University. Systems Optimization Laboratory
language : en
Publisher:
Release Date : 1979
Algorithms For Nonlinearly Constrained Optimization written by Stanford University. Systems Optimization Laboratory and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with categories.
Numerical Optimization 1984
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Author : Paul T. Boggs
language : en
Publisher: SIAM
Release Date : 1985-01-01
Numerical Optimization 1984 written by Paul T. Boggs and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-01-01 with Mathematics categories.
Numerical Methods For Nonlinearly Constrained Optimization
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Author : Margaret Ann Hagen Wright
language : en
Publisher:
Release Date : 1976
Numerical Methods For Nonlinearly Constrained Optimization written by Margaret Ann Hagen Wright and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Algorithms categories.
Numerical Aspects Of Trajectory Algorithms For Nonlinearly Constrained Optimization
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Author : Stanford University. Department of Operations Research. Systems Optimization Laboratory
language : en
Publisher:
Release Date : 1976
Numerical Aspects Of Trajectory Algorithms For Nonlinearly Constrained Optimization written by Stanford University. Department of Operations Research. Systems Optimization Laboratory and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with categories.
This paper discusses two algorithms for nonlinearly constrained optimization. These algorithms -- the penalty and barrier trajectory algorithms -- are based on an examination of the trajectories of approach to the solution that characterize the quadratic penalty function and the logarithmic barrier function, respectively. Although closely related in principle, the two algorithms display important differences in their implementation as well as in the properties of the generated iterates. The discussion will emphasize the numerical aspects of implementation of the trajectory algorithms, with particular attention to the choice of reliable methods for carrying out the required computations. (Author).
Practical Methods Of Optimization
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Author : R. Fletcher
language : en
Publisher: John Wiley & Sons
Release Date : 2013-06-06
Practical Methods Of Optimization written by R. Fletcher and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-06 with Mathematics categories.
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.
Nonlinear Programming
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Author : Mokhtar S. Bazaraa
language : en
Publisher: John Wiley & Sons
Release Date : 2013-06-12
Nonlinear Programming written by Mokhtar S. Bazaraa and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-12 with Mathematics categories.
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.
Nonlinear Optimization With Engineering Applications
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Author : Michael Bartholomew-Biggs
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-12-16
Nonlinear Optimization With Engineering Applications written by Michael Bartholomew-Biggs and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-16 with Mathematics categories.
This book, like its companion volume Nonlinear Optimization with Financial Applications, is an outgrowth of undergraduate and po- graduate courses given at the University of Hertfordshire and the University of Bergamo. It deals with the theory behind numerical methods for nonlinear optimization and their application to a range of problems in science and engineering. The book is intended for ?nal year undergraduate students in mathematics (or other subjects with a high mathematical or computational content) and exercises are provided at the end of most sections. The material should also be useful for postg- duate students and other researchers and practitioners who may be c- cerned with the development or use of optimization algorithms. It is assumed that readers have an understanding of the algebra of matrices and vectors and of the Taylor and mean value theorems in several va- ables. Prior experience of using computational techniques for solving systems of linear equations is also desirable, as is familiarity with the behaviour of iterative algorithms such as Newton’s methodfor nonlinear equations in one variable. Most of the currently popular methods for continuous nonlinear optimization are described and given (at least) an intuitive justi?cation. Relevant convergence results are also outlined and we provide proofs of these when it seems instructive to do so. This theoretical material is complemented by numerical illustrations which give a ?avour of how the methods perform in practice.