Introduction to the theory of nonlinear optimization:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cham, Switzerland
Springer
[2020]
|
| Edition: | Fourth edition |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Inhaltsverzeichnis Inhaltsverzeichnis |
| Physical Description: | x, 323 Seiten Illustrationen |
| ISBN: | 9783030427627 9783030427597 |
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Record in the Search Index
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1 Introduction and ProblemFormulation. 1 2 Existence Theorems for MinimalPoints. 2.1 Problem Formulation. 2.2 Existence Theorems. 2.3 Set of Minimal Points. 2.4 Application to Approximation Problems. 2.5 Application to Optimal Control Problems. Exercises. 9 9 10 20 21 25 31 3 Generalized Derivatives. 3.1 Directional Derivative. 3.2 Gâteaux and Frédiét Derivatives. 3.3 Subdifferential. 3.4 Quasidifferential. 3.5 Clarke Derivative. Exercises. 33 33 39 50 58 68 75 4 Tangent
Cones. 79 4.1 Definition and Properties. 79 4.2 Optimality Conditions. 90 4.3 A Lyusternik Theorem. 97 Exercises. 105 5 Generalized Lagrange Multiplier Rule. 5.1 Problem Formulation. 5.2 Necessary Optimality Conditions. 5.3 Sufficient Optimality Conditions. 5.4 Application to Optimal Control Problems. Exercises. 107 107 110 128 138 157 6 Duality. 6.1 Problem Formulation. 6.2 Duality Theorems. 6.3 Saddle Point Theorems. 161 161 168 171 ix
x Contents 6.4 Linear Problems. 175 6.5 Application to Approximation Problems . 178 Exercises. 187 7 Application to Extended Semidefinite Optimization. 7.1 Löwner Ordering Cone and Extensions. 7.2 Optimality Conditions. 7.3 Duality. Exercises. 189 189 203 207 209 8 Extension to Discrete-Continuous Problems. 8.1 Problem Formulation. 8.2 Separation Theorems for Discrete Sets . 8.3 Optimality Conditions. 8.3.1 Specialization to Discrete Sets with Finite Cardinality. 8.4 Duality. 8.4.1 Specialization to Extendedly Linear Problems. 8.5 Application to Discrete-Continuous Semidefinite and Copositive Optimization.
Exercises. 213 213 215 223 232 240 242 9 Direct Treatment of Special Optimization Problems. 9.1 Linear Quadratic Optimal Control Problems. 9.2 Time Minimal Control Problems. Exercises. 253 253 261 278 A Weak Convergence. 281 В Reflexivity of Banach Spaces. 283 247 250 C Hahn-Banach Theorem . 285 D Partially Ordered Linear Spaces. 289 Answers to the Exercises. 293 Bibliography. 309 Index. 321
1 Introduction and ProblemFormulation. 1 2 Existence Theorems for MinimalPoints. 2.1 Problem Formulation. 2.2 Existence Theorems. 2.3 Set of Minimal Points. 2.4 Application to Approximation Problems. 2.5 Application to Optimal Control Problems. Exercises. 9 9 10 20 21 25 31 3 Generalized Derivatives. 3.1 Directional Derivative. 3.2 Gâteaux and Frédiét Derivatives. 3.3 Subdifferential. 3.4 Quasidifferential. 3.5 Clarke Derivative. Exercises. 33 33 39 50 58 68 75 4 Tangent
Cones. 79 4.1 Definition and Properties. 79 4.2 Optimality Conditions. 90 4.3 A Lyusternik Theorem. 97 Exercises. 105 5 Generalized Lagrange Multiplier Rule. 5.1 Problem Formulation. 5.2 Necessary Optimality Conditions. 5.3 Sufficient Optimality Conditions. 5.4 Application to Optimal Control Problems. Exercises. 107 107 110 128 138 157 6 Duality. 6.1 Problem Formulation. 6.2 Duality Theorems. 6.3 Saddle Point Theorems. 161 161 168 171 ix
x Contents 6.4 Linear Problems. 175 6.5 Application to Approximation Problems . 178 Exercises. 187 7 Application to Extended Semidefinite Optimization. 7.1 Löwner Ordering Cone and Extensions. 7.2 Optimality Conditions. 7.3 Duality. Exercises. 189 189 203 207 209 8 Extension to Discrete-Continuous Problems. 8.1 Problem Formulation. 8.2 Separation Theorems for Discrete Sets . 8.3 Optimality Conditions. 8.3.1 Specialization to Discrete Sets with Finite Cardinality. 8.4 Duality. 8.4.1 Specialization to Extendedly Linear Problems. 8.5 Application to Discrete-Continuous Semidefinite and Copositive Optimization.
Exercises. 213 213 215 223 232 240 242 9 Direct Treatment of Special Optimization Problems. 9.1 Linear Quadratic Optimal Control Problems. 9.2 Time Minimal Control Problems. Exercises. 253 253 261 278 A Weak Convergence. 281 В Reflexivity of Banach Spaces. 283 247 250 C Hahn-Banach Theorem . 285 D Partially Ordered Linear Spaces. 289 Answers to the Exercises. 293 Bibliography. 309 Index. 321
1 Introduction and ProblemFormulation. 1 2 Existence Theorems for MinimalPoints. 2.1 Problem Formulation. 2.2 Existence Theorems. 2.3 Set of Minimal Points. 2.4 Application to Approximation Problems. 2.5 Application to Optimal Control Problems. Exercises. 9 9 10 20 21 25 31 3 Generalized Derivatives. 3.1 Directional Derivative. 3.2 Gâteaux and Frédiét Derivatives. 3.3 Subdifferential. 3.4 Quasidifferential. 3.5 Clarke Derivative. Exercises. 33 33 39 50 58 68 75 4 Tangent
Cones. 79 4.1 Definition and Properties. 79 4.2 Optimality Conditions. 90 4.3 A Lyusternik Theorem. 97 Exercises. 105 5 Generalized Lagrange Multiplier Rule. 5.1 Problem Formulation. 5.2 Necessary Optimality Conditions. 5.3 Sufficient Optimality Conditions. 5.4 Application to Optimal Control Problems. Exercises. 107 107 110 128 138 157 6 Duality. 6.1 Problem Formulation. 6.2 Duality Theorems. 6.3 Saddle Point Theorems. 161 161 168 171 ix
x Contents 6.4 Linear Problems. 175 6.5 Application to Approximation Problems . 178 Exercises. 187 7 Application to Extended Semidefinite Optimization. 7.1 Löwner Ordering Cone and Extensions. 7.2 Optimality Conditions. 7.3 Duality. Exercises. 189 189 203 207 209 8 Extension to Discrete-Continuous Problems. 8.1 Problem Formulation. 8.2 Separation Theorems for Discrete Sets . 8.3 Optimality Conditions. 8.3.1 Specialization to Discrete Sets with Finite Cardinality. 8.4 Duality. 8.4.1 Specialization to Extendedly Linear Problems. 8.5 Application to Discrete-Continuous Semidefinite and Copositive Optimization.
Exercises. 213 213 215 223 232 240 242 9 Direct Treatment of Special Optimization Problems. 9.1 Linear Quadratic Optimal Control Problems. 9.2 Time Minimal Control Problems. Exercises. 253 253 261 278 A Weak Convergence. 281 В Reflexivity of Banach Spaces. 283 247 250 C Hahn-Banach Theorem . 285 D Partially Ordered Linear Spaces. 289 Answers to the Exercises. 293 Bibliography. 309 Index. 321 |
| adam_txt |
1 Introduction and ProblemFormulation. 1 2 Existence Theorems for MinimalPoints. 2.1 Problem Formulation. 2.2 Existence Theorems. 2.3 Set of Minimal Points. 2.4 Application to Approximation Problems. 2.5 Application to Optimal Control Problems. Exercises. 9 9 10 20 21 25 31 3 Generalized Derivatives. 3.1 Directional Derivative. 3.2 Gâteaux and Frédiét Derivatives. 3.3 Subdifferential. 3.4 Quasidifferential. 3.5 Clarke Derivative. Exercises. 33 33 39 50 58 68 75 4 Tangent
Cones. 79 4.1 Definition and Properties. 79 4.2 Optimality Conditions. 90 4.3 A Lyusternik Theorem. 97 Exercises. 105 5 Generalized Lagrange Multiplier Rule. 5.1 Problem Formulation. 5.2 Necessary Optimality Conditions. 5.3 Sufficient Optimality Conditions. 5.4 Application to Optimal Control Problems. Exercises. 107 107 110 128 138 157 6 Duality. 6.1 Problem Formulation. 6.2 Duality Theorems. 6.3 Saddle Point Theorems. 161 161 168 171 ix
x Contents 6.4 Linear Problems. 175 6.5 Application to Approximation Problems . 178 Exercises. 187 7 Application to Extended Semidefinite Optimization. 7.1 Löwner Ordering Cone and Extensions. 7.2 Optimality Conditions. 7.3 Duality. Exercises. 189 189 203 207 209 8 Extension to Discrete-Continuous Problems. 8.1 Problem Formulation. 8.2 Separation Theorems for Discrete Sets . 8.3 Optimality Conditions. 8.3.1 Specialization to Discrete Sets with Finite Cardinality. 8.4 Duality. 8.4.1 Specialization to Extendedly Linear Problems. 8.5 Application to Discrete-Continuous Semidefinite and Copositive Optimization.
Exercises. 213 213 215 223 232 240 242 9 Direct Treatment of Special Optimization Problems. 9.1 Linear Quadratic Optimal Control Problems. 9.2 Time Minimal Control Problems. Exercises. 253 253 261 278 A Weak Convergence. 281 В Reflexivity of Banach Spaces. 283 247 250 C Hahn-Banach Theorem . 285 D Partially Ordered Linear Spaces. 289 Answers to the Exercises. 293 Bibliography. 309 Index. 321
1 Introduction and ProblemFormulation. 1 2 Existence Theorems for MinimalPoints. 2.1 Problem Formulation. 2.2 Existence Theorems. 2.3 Set of Minimal Points. 2.4 Application to Approximation Problems. 2.5 Application to Optimal Control Problems. Exercises. 9 9 10 20 21 25 31 3 Generalized Derivatives. 3.1 Directional Derivative. 3.2 Gâteaux and Frédiét Derivatives. 3.3 Subdifferential. 3.4 Quasidifferential. 3.5 Clarke Derivative. Exercises. 33 33 39 50 58 68 75 4 Tangent
Cones. 79 4.1 Definition and Properties. 79 4.2 Optimality Conditions. 90 4.3 A Lyusternik Theorem. 97 Exercises. 105 5 Generalized Lagrange Multiplier Rule. 5.1 Problem Formulation. 5.2 Necessary Optimality Conditions. 5.3 Sufficient Optimality Conditions. 5.4 Application to Optimal Control Problems. Exercises. 107 107 110 128 138 157 6 Duality. 6.1 Problem Formulation. 6.2 Duality Theorems. 6.3 Saddle Point Theorems. 161 161 168 171 ix
x Contents 6.4 Linear Problems. 175 6.5 Application to Approximation Problems . 178 Exercises. 187 7 Application to Extended Semidefinite Optimization. 7.1 Löwner Ordering Cone and Extensions. 7.2 Optimality Conditions. 7.3 Duality. Exercises. 189 189 203 207 209 8 Extension to Discrete-Continuous Problems. 8.1 Problem Formulation. 8.2 Separation Theorems for Discrete Sets . 8.3 Optimality Conditions. 8.3.1 Specialization to Discrete Sets with Finite Cardinality. 8.4 Duality. 8.4.1 Specialization to Extendedly Linear Problems. 8.5 Application to Discrete-Continuous Semidefinite and Copositive Optimization.
Exercises. 213 213 215 223 232 240 242 9 Direct Treatment of Special Optimization Problems. 9.1 Linear Quadratic Optimal Control Problems. 9.2 Time Minimal Control Problems. Exercises. 253 253 261 278 A Weak Convergence. 281 В Reflexivity of Banach Spaces. 283 247 250 C Hahn-Banach Theorem . 285 D Partially Ordered Linear Spaces. 289 Answers to the Exercises. 293 Bibliography. 309 Index. 321
1 Introduction and ProblemFormulation. 1 2 Existence Theorems for MinimalPoints. 2.1 Problem Formulation. 2.2 Existence Theorems. 2.3 Set of Minimal Points. 2.4 Application to Approximation Problems. 2.5 Application to Optimal Control Problems. Exercises. 9 9 10 20 21 25 31 3 Generalized Derivatives. 3.1 Directional Derivative. 3.2 Gâteaux and Frédiét Derivatives. 3.3 Subdifferential. 3.4 Quasidifferential. 3.5 Clarke Derivative. Exercises. 33 33 39 50 58 68 75 4 Tangent
Cones. 79 4.1 Definition and Properties. 79 4.2 Optimality Conditions. 90 4.3 A Lyusternik Theorem. 97 Exercises. 105 5 Generalized Lagrange Multiplier Rule. 5.1 Problem Formulation. 5.2 Necessary Optimality Conditions. 5.3 Sufficient Optimality Conditions. 5.4 Application to Optimal Control Problems. Exercises. 107 107 110 128 138 157 6 Duality. 6.1 Problem Formulation. 6.2 Duality Theorems. 6.3 Saddle Point Theorems. 161 161 168 171 ix
x Contents 6.4 Linear Problems. 175 6.5 Application to Approximation Problems . 178 Exercises. 187 7 Application to Extended Semidefinite Optimization. 7.1 Löwner Ordering Cone and Extensions. 7.2 Optimality Conditions. 7.3 Duality. Exercises. 189 189 203 207 209 8 Extension to Discrete-Continuous Problems. 8.1 Problem Formulation. 8.2 Separation Theorems for Discrete Sets . 8.3 Optimality Conditions. 8.3.1 Specialization to Discrete Sets with Finite Cardinality. 8.4 Duality. 8.4.1 Specialization to Extendedly Linear Problems. 8.5 Application to Discrete-Continuous Semidefinite and Copositive Optimization.
Exercises. 213 213 215 223 232 240 242 9 Direct Treatment of Special Optimization Problems. 9.1 Linear Quadratic Optimal Control Problems. 9.2 Time Minimal Control Problems. Exercises. 253 253 261 278 A Weak Convergence. 281 В Reflexivity of Banach Spaces. 283 247 250 C Hahn-Banach Theorem . 285 D Partially Ordered Linear Spaces. 289 Answers to the Exercises. 293 Bibliography. 309 Index. 321 |
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| index_date | 2024-07-03T15:46:55Z |
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| language | English |
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| spelling | Jahn, Johannes 1951- Verfasser (DE-588)104274905 aut Introduction to the theory of nonlinear optimization Johannes Jahn Fourth edition Cham, Switzerland Springer [2020] x, 323 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Operations Research/Decision Theory Optimization Computational Intelligence Operations research Decision making Mathematical optimization Computational intelligence Nichtlineare Optimierung (DE-588)4128192-5 gnd rswk-swf Nichtlineare Optimierung (DE-588)4128192-5 s DE-604 Erscheint auch als Online-Ausgabe 978-3-030-42760-3 Digitalisierung UB Augsburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032377932&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Augsburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032377932&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Augsburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032377932&sequence=000005&line_number=0003&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Jahn, Johannes 1951- Introduction to the theory of nonlinear optimization Operations Research/Decision Theory Optimization Computational Intelligence Operations research Decision making Mathematical optimization Computational intelligence Nichtlineare Optimierung (DE-588)4128192-5 gnd |
| subject_GND | (DE-588)4128192-5 |
| title | Introduction to the theory of nonlinear optimization |
| title_auth | Introduction to the theory of nonlinear optimization |
| title_exact_search | Introduction to the theory of nonlinear optimization |
| title_exact_search_txtP | Introduction to the theory of nonlinear optimization |
| title_full | Introduction to the theory of nonlinear optimization Johannes Jahn |
| title_fullStr | Introduction to the theory of nonlinear optimization Johannes Jahn |
| title_full_unstemmed | Introduction to the theory of nonlinear optimization Johannes Jahn |
| title_short | Introduction to the theory of nonlinear optimization |
| title_sort | introduction to the theory of nonlinear optimization |
| topic | Operations Research/Decision Theory Optimization Computational Intelligence Operations research Decision making Mathematical optimization Computational intelligence Nichtlineare Optimierung (DE-588)4128192-5 gnd |
| topic_facet | Operations Research/Decision Theory Optimization Computational Intelligence Operations research Decision making Mathematical optimization Computational intelligence Nichtlineare Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032377932&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032377932&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032377932&sequence=000005&line_number=0003&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT jahnjohannes introductiontothetheoryofnonlinearoptimization |
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