Nonlinear programming: theory and algorithms
"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 se...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Hoboken, NJ
Wiley-Interscience
2006
|
| Edition: | 3. ed. |
| Subjects: | |
| Online Access: | Publisher description Inhaltsverzeichnis |
| Summary: | "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."--BOOK JACKET. |
| Item Description: | Literaturverz.: S. 779 - 841 |
| Physical Description: | XV, 853 Seiten Illustrationen, Diagramme |
| ISBN: | 0471486000 9780471486008 |
Staff View
MARC
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| 250 | |a 3. ed. | ||
| 264 | 1 | |a Hoboken, NJ |b Wiley-Interscience |c 2006 | |
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| 650 | 4 | |a Programación no-lineal | |
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| 650 | 4 | |a Nonlinear programming | |
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Record in the Search Index
| _version_ | 1804135740769042432 |
|---|---|
| adam_text | CONTENTS CHAPTER 1 INTRODUCTION 1 1.1 PROBLEM STATEMENT AND BASIC
DEFINITIONS 2 1.2 ILLUSTRATIVE EXAMPLES 4 1.3 GUIDELINES FOR MODEL
CONSTRUCTION 26 EXERCISES 30 NOTES AND REFERENCES 34 PART 1 CONVEX
ANALYSIS 37 CHAPTER 2 CONVEX SETS 39 2.1 CONVEX HULLS 40 2.2
CLOSUREANDLNTERIOROFASET 45 2.3 WEIERSTRASS S THEOREM 48 2.4 SEPARATION
AND SUPPORT OF SETS 50 2.5 CONVEX CONES AND POLARITY 62 2.6 POLYHEDRAL
SETS, EXTREME POINTS, AND EXTREME DIRECTIONS 64 2.7 LINEAR PROGRAMMING
AND THE SIMPLEX METHOD 75 EXERCISES 86 NOTES AND REFERENCES 93 CHAPTER 3
CONVEX FUNCTIONS AND GENERALIZATIONS 97 3.1 DEFINITIONS AND BASIC
PROPERTIES 98 3.2 SUBGRADIENTS OF CONVEX FUNCTIONS 103 3.3
DIFFERENTIABLE CONVEX FUNCTIONS 109 3.4 MINIMA AND MAXIMA OF CONVEX
FUNCTIONS 123 3.5 GENERALIZATIONS OF CONVEX FUNCTIONS 134 EXERCISES 147
NOTES AND REFERENCES 1 59 PART 2 OPTIMALITY CONDITIONS AND DUALITY 163
CHAPTER 4 THE FRITZ JOHN AND KARUSH-KUHN-TUCKER OPTIMALITY CONDITIONS
165 4.1 UNCONSTRAINED PROBLEMS 166 4.2 PROBLEMS HAVING INEQUALITY
CONSTRAINTS 174 4.3 PROBLEMS HAVING INEQUALITY AND EQUALITY CONSTRAINTS
197 4.4 SECOND-ORDER NECESSARY AND SUFFICIENT OPTIMALITY CONDITIONS FOR
CONSTRAINED PROBLEMS 211 EXERCISES 220 NOTES AND REFERENCES 235 CHAPTER
5 CONSTRAINT QUALIFICATIONS 237 5.1 CONEOFTANGENTS 237 5.2 OTHER
CONSTRAINT QUALIFICATIONS 241 5.3 PROBLEMS HAVING INEQUALITY AND
EQUALITY CONSTRAINTS 245 EXERCISES 250 NOTES AND REFERENCES 256 VII VIII
CONTENTS CHAPTER 6 LAGRANGIAN DUALITY AND SADDLE POINT OPTIMALITY
CONDITIONS 257 6.1 LAGRANGIAN DUAL PROBLEM 258 6.2 DUALITY THEOREMS AND
SADDLE POINT OPTIMALITY CONDITIONS 263 6.3 PROPERTIESOFTHE DUAL FUNCTION
276 6.4 FORMULATING AND SOLVING THE DUAL PROBLEM 286 6.5 GETTING THE
PRIMAL SOLUTION 293 6.6 LINEAR AND QUADRATIC PROGRAMS 298 EXERCISES 300
NOTES AND REFERENCES 313 PART 3 ALGORITHMS AND THEIR CONVERGENCE 315
CHAPTER 7 THECONCEPT OF AN ALGORITHRA 317 7.1 ALGORITHMS AND ALGORITHMIC
MAPS 317 7.2 CLOSED MAPS AND CONVERGENCE 319 7.3 COMPOSITUM OFMAPPINGS
324 7.4 COMPARISON AMONG ALGORITHMS 329 EXERCISES 332 NOTES AND
REFERENCES 340 CHAPTER 8 UNCONSTRAINED OPTIMIZATION 343 8.1 LINE SEARCH
WITHOUT USING DERIVATIVES 344 8.2 LINE SEARCH USING DERIVATIVES 356 8.3
SOME PRACTICAL LINE SEARCH METHODS 360 8.4 CLOSEDNESS OF THE LINE SEARCH
ALGORITHMIC MAP 363 8.5 MULTIDIMENSIONAL SEARCH WITHOUT USING
DERIVATIVES 365 8.6 MULTIDIMENSIONAL SEARCH USING DERIVATIVES 384 8.7
MODIFICATION OF NEWTON S METHOD: LEVENBERG-MARQUARDT AND TRUST REGION
METHODS 398 8.8 METHODS USING CONJUGATE DIRECTIONS: QUASI-NEWTON AND
CONJUGATE GRADIENT METHODS 402 8.9 SUBGRADIENT OPTIMIZATION METHODS 435
EXERCISES 444 NOTES AND REFERENCES 462 CHAPTER 9 PENALTY AND BARRIER
FUNCTIONS 469 9.1 CONCEPTOF PENALTY FUNCTIONS 470 9.2 EXTERIOR PENALTY
FUNCTION METHODS 475 9.3 EXACT ABSOLUTE VALUE AND AUGMENTED LAGRANGIAN
PENALTY METHODS 485 9.4 BARRIER FUNCTION METHODS 501 9.5 POLYNOMIAL-TIME
INTERIOR POINT ALGORITHMS FOR LINEAR PROGRAMMING BASED ON A BARRIER
FUNCTION 509 EXERCISES 520 NOTES AND REFERENCES 533 CHAPTER 10 METHODS
OF FEASIBLE DIRECTIONS 537 10.1 METHOD OFZOUTENDIJK 538 10.2 CONVERGENCE
ANALYSIS OF THE METHOD OF ZOUTENDIJK 557 10.3 SUCCESSIVE LINEAR
PROGRAMMING APPROACH 568 10.4 SUCCESSIVE QUADRATIC PROGRAMMING OR
PROJECTED LAGRANGIAN APPROACH 576 10.5 GRADIENT PROJECTION METHOD OF
ROSEN 589 CONTENTS IX 10.6 REDUCED GRADIENT METHOD OF WOLFE AND
GENERALIZED REDUCED GRADIENT METHOD 602 10.7 CONVEX-SIMPLEX METHOD
OFZANGWILL 613 10.8 EFFECTIVE FIRST- AND SECOND-ORDER VARIANTS OF THE
REDUCED GRADIENT METHOD 620 EXERCISES 625 NOTES AND REFERENCES 649
CHAPTER 11 LINEAR COMPLEMENTARY PROBLEM, AND QUADRATIC, SEPARABLE,
FRACTIONAL, AND GEOMETRIE PROGRAMMING 655 11.1 LINEAR COMPLEMENTARY
PROBLEM 656 11.2 CONVEX AND NONCONVEX QUADRATIC PROGRAMMING: GLOBAL
OPTIMIZATION APPROACHES 667 11.3 SEPARABLE PROGRAMMING 684 11.4 LINEAR
FRACTIONAL PROGRAMMING 703 11.5 GEOMETRIE PROGRAMMING 712 EXERCISES 722
NOTES AND REFERENCES 745 APPENDIX A MATHEMATICAL REVIEW 751 APPENDIX B
SUMMARY OF CONVEXITY, OPTIMALITY CONDITIONS, AND DUALITY 765
BIBLIOGRAPHY 779 INDEX 843
|
| adam_txt |
CONTENTS CHAPTER 1 INTRODUCTION 1 1.1 PROBLEM STATEMENT AND BASIC
DEFINITIONS 2 1.2 ILLUSTRATIVE EXAMPLES 4 1.3 GUIDELINES FOR MODEL
CONSTRUCTION 26 EXERCISES 30 NOTES AND REFERENCES 34 PART 1 CONVEX
ANALYSIS 37 CHAPTER 2 CONVEX SETS 39 2.1 CONVEX HULLS 40 2.2
CLOSUREANDLNTERIOROFASET 45 2.3 WEIERSTRASS'S THEOREM 48 2.4 SEPARATION
AND SUPPORT OF SETS 50 2.5 CONVEX CONES AND POLARITY 62 2.6 POLYHEDRAL
SETS, EXTREME POINTS, AND EXTREME DIRECTIONS 64 2.7 LINEAR PROGRAMMING
AND THE SIMPLEX METHOD 75 EXERCISES 86 NOTES AND REFERENCES 93 CHAPTER 3
CONVEX FUNCTIONS AND GENERALIZATIONS 97 3.1 DEFINITIONS AND BASIC
PROPERTIES 98 3.2 SUBGRADIENTS OF CONVEX FUNCTIONS 103 3.3
DIFFERENTIABLE CONVEX FUNCTIONS 109 3.4 MINIMA AND MAXIMA OF CONVEX
FUNCTIONS 123 3.5 GENERALIZATIONS OF CONVEX FUNCTIONS 134 EXERCISES 147
NOTES AND REFERENCES 1 59 PART 2 OPTIMALITY CONDITIONS AND DUALITY 163
CHAPTER 4 THE FRITZ JOHN AND KARUSH-KUHN-TUCKER OPTIMALITY CONDITIONS
165 4.1 UNCONSTRAINED PROBLEMS 166 4.2 PROBLEMS HAVING INEQUALITY
CONSTRAINTS 174 4.3 PROBLEMS HAVING INEQUALITY AND EQUALITY CONSTRAINTS
197 4.4 SECOND-ORDER NECESSARY AND SUFFICIENT OPTIMALITY CONDITIONS FOR
CONSTRAINED PROBLEMS 211 EXERCISES 220 NOTES AND REFERENCES 235 CHAPTER
5 CONSTRAINT QUALIFICATIONS 237 5.1 CONEOFTANGENTS 237 5.2 OTHER
CONSTRAINT QUALIFICATIONS 241 5.3 PROBLEMS HAVING INEQUALITY AND
EQUALITY CONSTRAINTS 245 EXERCISES 250 NOTES AND REFERENCES 256 VII VIII
CONTENTS CHAPTER 6 LAGRANGIAN DUALITY AND SADDLE POINT OPTIMALITY
CONDITIONS 257 6.1 LAGRANGIAN DUAL PROBLEM 258 6.2 DUALITY THEOREMS AND
SADDLE POINT OPTIMALITY CONDITIONS 263 6.3 PROPERTIESOFTHE DUAL FUNCTION
276 6.4 FORMULATING AND SOLVING THE DUAL PROBLEM 286 6.5 GETTING THE
PRIMAL SOLUTION 293 6.6 LINEAR AND QUADRATIC PROGRAMS 298 EXERCISES 300
NOTES AND REFERENCES 313 PART 3 ALGORITHMS AND THEIR CONVERGENCE 315
CHAPTER 7 THECONCEPT OF AN ALGORITHRA 317 7.1 ALGORITHMS AND ALGORITHMIC
MAPS 317 7.2 CLOSED MAPS AND CONVERGENCE 319 7.3 COMPOSITUM OFMAPPINGS
324 7.4 COMPARISON AMONG ALGORITHMS 329 EXERCISES 332 NOTES AND
REFERENCES 340 CHAPTER 8 UNCONSTRAINED OPTIMIZATION 343 8.1 LINE SEARCH
WITHOUT USING DERIVATIVES 344 8.2 LINE SEARCH USING DERIVATIVES 356 8.3
SOME PRACTICAL LINE SEARCH METHODS 360 8.4 CLOSEDNESS OF THE LINE SEARCH
ALGORITHMIC MAP 363 8.5 MULTIDIMENSIONAL SEARCH WITHOUT USING
DERIVATIVES 365 8.6 MULTIDIMENSIONAL SEARCH USING DERIVATIVES 384 8.7
MODIFICATION OF NEWTON'S METHOD: LEVENBERG-MARQUARDT AND TRUST REGION
METHODS 398 8.8 METHODS USING CONJUGATE DIRECTIONS: QUASI-NEWTON AND
CONJUGATE GRADIENT METHODS 402 8.9 SUBGRADIENT OPTIMIZATION METHODS 435
EXERCISES 444 NOTES AND REFERENCES 462 CHAPTER 9 PENALTY AND BARRIER
FUNCTIONS 469 9.1 CONCEPTOF PENALTY FUNCTIONS 470 9.2 EXTERIOR PENALTY
FUNCTION METHODS 475 9.3 EXACT ABSOLUTE VALUE AND AUGMENTED LAGRANGIAN
PENALTY METHODS 485 9.4 BARRIER FUNCTION METHODS 501 9.5 POLYNOMIAL-TIME
INTERIOR POINT ALGORITHMS FOR LINEAR PROGRAMMING BASED ON A BARRIER
FUNCTION 509 EXERCISES 520 NOTES AND REFERENCES 533 CHAPTER 10 METHODS
OF FEASIBLE DIRECTIONS 537 10.1 METHOD OFZOUTENDIJK 538 10.2 CONVERGENCE
ANALYSIS OF THE METHOD OF ZOUTENDIJK 557 10.3 SUCCESSIVE LINEAR
PROGRAMMING APPROACH 568 10.4 SUCCESSIVE QUADRATIC PROGRAMMING OR
PROJECTED LAGRANGIAN APPROACH 576 10.5 GRADIENT PROJECTION METHOD OF
ROSEN 589 CONTENTS IX 10.6 REDUCED GRADIENT METHOD OF WOLFE AND
GENERALIZED REDUCED GRADIENT METHOD 602 10.7 CONVEX-SIMPLEX METHOD
OFZANGWILL 613 10.8 EFFECTIVE FIRST- AND SECOND-ORDER VARIANTS OF THE
REDUCED GRADIENT METHOD 620 EXERCISES 625 NOTES AND REFERENCES 649
CHAPTER 11 LINEAR COMPLEMENTARY PROBLEM, AND QUADRATIC, SEPARABLE,
FRACTIONAL, AND GEOMETRIE PROGRAMMING 655 11.1 LINEAR COMPLEMENTARY
PROBLEM 656 11.2 CONVEX AND NONCONVEX QUADRATIC PROGRAMMING: GLOBAL
OPTIMIZATION APPROACHES 667 11.3 SEPARABLE PROGRAMMING 684 11.4 LINEAR
FRACTIONAL PROGRAMMING 703 11.5 GEOMETRIE PROGRAMMING 712 EXERCISES 722
NOTES AND REFERENCES 745 APPENDIX A MATHEMATICAL REVIEW 751 APPENDIX B
SUMMARY OF CONVEXITY, OPTIMALITY CONDITIONS, AND DUALITY 765
BIBLIOGRAPHY 779 INDEX 843 |
| any_adam_object | 1 |
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| author | Bazaraa, Mokhtar S. 1943- Sherali, Hanif D. 1952- Shetty, Chitharanjan M. 1929- |
| author_GND | (DE-588)13576856X (DE-588)135768586 (DE-588)135768608 |
| author_facet | Bazaraa, Mokhtar S. 1943- Sherali, Hanif D. 1952- Shetty, Chitharanjan M. 1929- |
| author_role | aut aut aut |
| author_sort | Bazaraa, Mokhtar S. 1943- |
| author_variant | m s b ms msb h d s hd hds c m s cm cms |
| building | Verbundindex |
| bvnumber | BV021817109 |
| callnumber-first | T - Technology |
| callnumber-label | T57 |
| callnumber-raw | T57.8 |
| callnumber-search | T57.8 |
| callnumber-sort | T 257.8 |
| callnumber-subject | T - General Technology |
| classification_rvk | QH 421 SK 870 |
| classification_tum | MAT 916f |
| ctrlnum | (OCoLC)61478842 (DE-599)BVBBV021817109 |
| dewey-full | 519.7/6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.7/6 |
| dewey-search | 519.7/6 |
| dewey-sort | 3519.7 16 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Mathematik Wirtschaftswissenschaften |
| edition | 3. ed. |
| format | Book |
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| id | DE-604.BV021817109 |
| illustrated | Illustrated |
| index_date | 2024-07-02T15:52:49Z |
| indexdate | 2024-07-09T20:45:19Z |
| institution | BVB |
| isbn | 0471486000 9780471486008 |
| language | English |
| lccn | 2005054230 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015029310 |
| oclc_num | 61478842 |
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| owner_facet | DE-824 DE-91 DE-BY-TUM DE-29T DE-384 DE-634 DE-83 DE-898 DE-BY-UBR DE-739 |
| physical | XV, 853 Seiten Illustrationen, Diagramme |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Wiley-Interscience |
| record_format | marc |
| spelling | Bazaraa, Mokhtar S. 1943- Verfasser (DE-588)13576856X aut Nonlinear programming theory and algorithms Mokhtar S. Bazaraa ; Hanif D. Sherali ; C. M. Shetty 3. ed. Hoboken, NJ Wiley-Interscience 2006 XV, 853 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Literaturverz.: S. 779 - 841 "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."--BOOK JACKET. Programación no-lineal Programmation non linéaire Nonlinear programming Nichtlineare Optimierung (DE-588)4128192-5 gnd rswk-swf Optimierung (DE-588)4043664-0 gnd rswk-swf Optimierung (DE-588)4043664-0 s Nichtlineare Optimierung (DE-588)4128192-5 s 1\p DE-604 Sherali, Hanif D. 1952- Verfasser (DE-588)135768586 aut Shetty, Chitharanjan M. 1929- Verfasser (DE-588)135768608 aut http://www.loc.gov/catdir/enhancements/fy0625/2005054230-d.html Publisher description GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015029310&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bazaraa, Mokhtar S. 1943- Sherali, Hanif D. 1952- Shetty, Chitharanjan M. 1929- Nonlinear programming theory and algorithms Programación no-lineal Programmation non linéaire Nonlinear programming Nichtlineare Optimierung (DE-588)4128192-5 gnd Optimierung (DE-588)4043664-0 gnd |
| subject_GND | (DE-588)4128192-5 (DE-588)4043664-0 |
| title | Nonlinear programming theory and algorithms |
| title_auth | Nonlinear programming theory and algorithms |
| title_exact_search | Nonlinear programming theory and algorithms |
| title_exact_search_txtP | Nonlinear programming theory and algorithms |
| title_full | Nonlinear programming theory and algorithms Mokhtar S. Bazaraa ; Hanif D. Sherali ; C. M. Shetty |
| title_fullStr | Nonlinear programming theory and algorithms Mokhtar S. Bazaraa ; Hanif D. Sherali ; C. M. Shetty |
| title_full_unstemmed | Nonlinear programming theory and algorithms Mokhtar S. Bazaraa ; Hanif D. Sherali ; C. M. Shetty |
| title_short | Nonlinear programming |
| title_sort | nonlinear programming theory and algorithms |
| title_sub | theory and algorithms |
| topic | Programación no-lineal Programmation non linéaire Nonlinear programming Nichtlineare Optimierung (DE-588)4128192-5 gnd Optimierung (DE-588)4043664-0 gnd |
| topic_facet | Programación no-lineal Programmation non linéaire Nonlinear programming Nichtlineare Optimierung Optimierung |
| url | http://www.loc.gov/catdir/enhancements/fy0625/2005054230-d.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015029310&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT bazaraamokhtars nonlinearprogrammingtheoryandalgorithms AT sheralihanifd nonlinearprogrammingtheoryandalgorithms AT shettychitharanjanm nonlinearprogrammingtheoryandalgorithms |