Rigorous global search: continuous problems
The book provides a self-contained introduction to underlying techniques, as well as a compendium of theory and a guide to the author's Fortran 90 software for nonlinear algebraic systems and global, constrained optimization with automatic result verification. Besides introductory and survey ma...
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht [u.a.]
Kluwer Acad. Publ.
1996
|
| Series: | Nonconvex optimization and its applications
13 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Summary: | The book provides a self-contained introduction to underlying techniques, as well as a compendium of theory and a guide to the author's Fortran 90 software for nonlinear algebraic systems and global, constrained optimization with automatic result verification. Besides introductory and survey material, the book contains unique research results. The book also contains non-traditional ideas concerning non-smooth optimization. Thus, the book should be a valuable reference to applied mathematicians and computational scientists and engineers. With numerous examples and exercises, as well as leads for future research, the book can be used as a graduate text or reference on interval arithmetic, automatic differentiation and interval fixed point theory The book can also serve as a user's guide for the nonlinear equations and optimization software, available free of charge from the author, for the author's general Fortran 90 interval arithmetic package, or for the associated automatic differentiation package. Audience: Researchers in operations research, numerical analysis, computational chemistry, computer-aided geometric design and computational geometry, robot kinematics, remote sensing. Also suitable for graduate and topics courses in numerical analysis, optimization, and operations research |
| Physical Description: | XV, 262 S. :graph. Darst. |
| ISBN: | 0792342380 |
Staff View
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| 490 | 1 | |a Nonconvex optimization and its applications |v 13 | |
| 520 | 3 | |a The book provides a self-contained introduction to underlying techniques, as well as a compendium of theory and a guide to the author's Fortran 90 software for nonlinear algebraic systems and global, constrained optimization with automatic result verification. Besides introductory and survey material, the book contains unique research results. The book also contains non-traditional ideas concerning non-smooth optimization. Thus, the book should be a valuable reference to applied mathematicians and computational scientists and engineers. With numerous examples and exercises, as well as leads for future research, the book can be used as a graduate text or reference on interval arithmetic, automatic differentiation and interval fixed point theory | |
| 520 | |a The book can also serve as a user's guide for the nonlinear equations and optimization software, available free of charge from the author, for the author's general Fortran 90 interval arithmetic package, or for the associated automatic differentiation package. Audience: Researchers in operations research, numerical analysis, computational chemistry, computer-aided geometric design and computational geometry, robot kinematics, remote sensing. Also suitable for graduate and topics courses in numerical analysis, optimization, and operations research | ||
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
LIST OF FIGURES vii
LIST OF TABLES xi
PREFACE xiii
1 PRELIMINARIES 1
1.1 Interval Arithmetic 3
1.2 Interval Linear Systems 18
1.3 Derivatives and Slopes 26
1.4 Automatic Differentiation and Code Lists 36
1.5 Interval Newton Methods and Interval Fixed Point Theory 50
1.6 The Topological Degree 66
2 SOFTWARE ENVIRONMENTS 71
2.1 INTLIB 71
2.2 Fortran 90 Interval and Code List Support 78
2.3 Other Software Environments 102
3 ON PRECONDITIONING 113
3.1 The Inverse Midpoint Preconditioner 115
3.2 Optimal Linear Programming Preconditioners 120
4 VERIFIED SOLUTION OF NONLINEAR
SYSTEMS 145
4.1 An Overall Branch and Bound Algorithm 146
4.2 Approximate Roots and Epsilon Inflation 150
v
vi Rigorous Global Search: Continuous Problems
4.3 Tessellation Schemes 154
4.4 Description of Provided Software 159
4.5 Alternate Algorithms and Improvements 167
5 OPTIMIZATION 169
5.1 Background and Historical Algorithms 170
5.2 Handling Constraints 177
5.3 Description of Provided Software 199
6 NON DIFFERENTIABLE PROBLEMS 209
6.1 Extensions of Non Smooth Functions 210
6.2 Use in Interval Newton Methods 218
7 USE OF INTERMEDIATE QUANTITIES IN
THE EXPRESSION VALUES 227
7.1 The Basic Approach 227
7.2 An Alternate Viewpoint Constraint Propagation 230
7.3 Application to Global Optimization 230
7.4 Efficiency and Practicality 232
7.5 Provided Software 233
7.6 Exercises 234
REFERENCES 235
INDEX 255
|
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| id | DE-604.BV011620717 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:12:52Z |
| institution | BVB |
| isbn | 0792342380 |
| language | English |
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| physical | XV, 262 S. :graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Kluwer Acad. Publ. |
| record_format | marc |
| series | Nonconvex optimization and its applications |
| series2 | Nonconvex optimization and its applications |
| spelling | Kearfott, R. B. Verfasser aut Rigorous global search continuous problems by R. Baker Kearfott Dordrecht [u.a.] Kluwer Acad. Publ. 1996 XV, 262 S. :graph. Darst. txt rdacontent n rdamedia nc rdacarrier Nonconvex optimization and its applications 13 The book provides a self-contained introduction to underlying techniques, as well as a compendium of theory and a guide to the author's Fortran 90 software for nonlinear algebraic systems and global, constrained optimization with automatic result verification. Besides introductory and survey material, the book contains unique research results. The book also contains non-traditional ideas concerning non-smooth optimization. Thus, the book should be a valuable reference to applied mathematicians and computational scientists and engineers. With numerous examples and exercises, as well as leads for future research, the book can be used as a graduate text or reference on interval arithmetic, automatic differentiation and interval fixed point theory The book can also serve as a user's guide for the nonlinear equations and optimization software, available free of charge from the author, for the author's general Fortran 90 interval arithmetic package, or for the associated automatic differentiation package. Audience: Researchers in operations research, numerical analysis, computational chemistry, computer-aided geometric design and computational geometry, robot kinematics, remote sensing. Also suitable for graduate and topics courses in numerical analysis, optimization, and operations research Niet-lineaire systemen gtt Optimaliseren gtt Mathematical optimization Nonlinear programming Globale Optimierung (DE-588)4140067-7 gnd rswk-swf Nichtkonvexe Optimierung (DE-588)4309215-9 gnd rswk-swf Globale Optimierung (DE-588)4140067-7 s Nichtkonvexe Optimierung (DE-588)4309215-9 s DE-604 Nonconvex optimization and its applications 13 (DE-604)BV010085908 13 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007829254&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kearfott, R. B. Rigorous global search continuous problems Nonconvex optimization and its applications Niet-lineaire systemen gtt Optimaliseren gtt Mathematical optimization Nonlinear programming Globale Optimierung (DE-588)4140067-7 gnd Nichtkonvexe Optimierung (DE-588)4309215-9 gnd |
| subject_GND | (DE-588)4140067-7 (DE-588)4309215-9 |
| title | Rigorous global search continuous problems |
| title_auth | Rigorous global search continuous problems |
| title_exact_search | Rigorous global search continuous problems |
| title_full | Rigorous global search continuous problems by R. Baker Kearfott |
| title_fullStr | Rigorous global search continuous problems by R. Baker Kearfott |
| title_full_unstemmed | Rigorous global search continuous problems by R. Baker Kearfott |
| title_short | Rigorous global search |
| title_sort | rigorous global search continuous problems |
| title_sub | continuous problems |
| topic | Niet-lineaire systemen gtt Optimaliseren gtt Mathematical optimization Nonlinear programming Globale Optimierung (DE-588)4140067-7 gnd Nichtkonvexe Optimierung (DE-588)4309215-9 gnd |
| topic_facet | Niet-lineaire systemen Optimaliseren Mathematical optimization Nonlinear programming Globale Optimierung Nichtkonvexe Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007829254&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV010085908 |
| work_keys_str_mv | AT kearfottrb rigorousglobalsearchcontinuousproblems |