Practical methods of optimization
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...
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| Hlavní autor: | |
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| Médium: | E-kniha Kniha |
| Jazyk: | angličtina |
| Vydáno: |
Chichester ; New York
Wiley
1987
John Wiley & Sons, Incorporated Wiley-Blackwell |
| Vydání: | 2 |
| Témata: | |
| ISBN: | 0471915475, 9780471915478, 0471494631, 9780471494638, 9781118723203, 1118723201 |
| On-line přístup: | Získat plný text |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Fletcher, R. (Roger) |
| Author_xml | – sequence: 1 fullname: Fletcher, R. (Roger) |
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| EISBN | 9781118723210 111872321X |
| Edition | 2 2nd ed. |
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| ISBN | 0471915475 9780471915478 0471494631 9780471494638 9781118723203 1118723201 |
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| Notes | Bibliography: p. [417]-429 Includes index A Wiley-Interscience publication. |
| OCLC | 848895470 |
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| PublicationDate | c1987 1988 2013-06-06 |
| PublicationDateYYYYMMDD | 1987-01-01 1988-01-01 2013-06-06 |
| PublicationDate_xml | – year: 1987 text: c1987 |
| PublicationDecade | 1980 2010 |
| PublicationPlace | Chichester ; New York |
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| PublicationYear | 1987 1988 2013 |
| Publisher | Wiley John Wiley & Sons, Incorporated Wiley-Blackwell |
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| Snippet | Fully describes optimization methods that are currently most valuable in solving real-life problems. Since optimization has applications in almost every branch... |
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| SubjectTerms | Mathematical optimization |
| TableOfContents | Cover -- Title Page -- Contents -- Preface -- Table of Notation -- PART 1 UNCONSTRAINED OPTIMIZATION -- Chapter 1 Introduction -- 1.1 History and Applications -- 1.2 Mathematical Background -- Questions for Chapter 1 -- Chapter 2 Structure of Methods -- 2.1 Conditions for Local Minima -- 2.2 Ad hoc Methods -- 2.3 Useful Algorithmic Properties -- 2.4 Quadratic Models -- 2.5 Descent Methods and Stability -- 2.6 Algorithms for the Line Search Subproblem -- Questions for Chapter 2 -- Chapter 3 Newton-like Methods -- 3.1 Newton's Method -- 3.2 Quasi-Newton Methods -- 3.3 Invariance -- 3.4 The Broyden Family -- 3.5 Numerical Experiments -- 3.6 Other Formulae -- Questions for Chapter 3 -- Chapter 4 Conjugate Direction Methods -- 4.1 Conjugate Gradient Methods -- 4.2 Direction Set Methods -- Questions for Chapter 4 -- Chapter 5 Restricted Step Methods -- 5.1 A Prototype Algorithm -- 5.2 Levenberg-Marquardt Methods -- Questions for Chapter 5 -- Chapter 6 Sums of Squares and Nonlinear Equations -- 6.1 Over-determined Systems -- 6.2 Well-determined Systems -- 6.3 No-derivative Methods -- Questions for Chapter 6 -- PART 2 CONSTRAINED OPTIMIZATION -- Chapter 7 Introduction -- 7.1 Preview -- 7.2 Elimination and Other Transformations -- Questions for Chapter 7 -- Chapter 8 Linear Programming -- 8.1 Structure -- 8.2 The Simplex Method -- 8.3 Other LP Techniques -- 8.4 Feasible Points for Linear Constraints -- 8.5 Stable and Large-scale Linear Programming -- 8.6 Degeneracy -- 8.7 Polynomial Time Algorithms -- Questions for Chapter 8 -- Chapter 9 The Theory of Constrained Optimization -- 9.1 Lagrange Multipliers -- 9.2 First Order Conditions -- 9.3 Second Order Conditions -- 9.4 Convexity -- 9.5 Duality -- Questions for Chapter 9 -- Chapter 10 Quadratic Programming -- 10.1 Equality Constraints -- 10.2 Lagrangian Methods -- 10.3 Active Set Methods 10.4 Advanced Features -- 10.5 Special QP Problems -- 10.6 Complementary Pivoting and Other Methods -- Questions for Chapter 10 -- Chapter 11 General Linearly Constrained Optimization -- 11.1 Equality Constraints -- 11.2 Inequality Constraints -- 11.3 Zigzagging -- Questions for Chapter 11 -- Chapter 12 Nonlinear Programming -- 12.1 Penalty and Barrier Functions -- 12.2 Multiplier Penalty Functions -- 12.3 The L1 Exact Penalty Function -- 12.4 The Lagrange-Newton Method (SQP) -- 12.5 Nonlinear Elimination and Feasible Direction Methods ... -- 12.6 Other Methods -- Questions for Chapter 12 -- Chapter 13 Other Optimization Problems -- 13.1 Integer Programming -- 13.2 Geometric Programming -- 13.3 Network Programming -- Questions for Chapter 13 -- Chapter 14 Non-Smooth Optimization -- 14.1 Introduction -- 14.2 Optimally Conditions -- 14.3 Exact Penalty Functions -- 14.4 Algorithms -- 14.5 A Globally Convergent Prototype Algorithm -- 14.6 Constrained Non-Smooth Optimization -- Questions for Chapter 14 -- References -- Subject Index |
| Title | Practical methods of optimization |
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