Aggregation in large-scale optimization:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht [u.a.]
Kluwer Academic Publ.
2003
|
| Series: | Applied optimization
83 |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | xii, 291 p. graph. Darst. |
| ISBN: | 1402075979 |
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| 245 | 1 | 0 | |a Aggregation in large-scale optimization |c by Igor Litvinchev and Vladimir Tsurkov |
| 264 | 1 | |a Dordrecht [u.a.] |b Kluwer Academic Publ. |c 2003 | |
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Record in the Search Index
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| adam_text | IMAGE 1
AGGREGATION IN LARGE-SCALE
OPTIMIZATION
BY IGOR LITVINCHEV
AND
VLADIMIR TSURKOV
COMPUTING CENTER, RUSSIAN ACADEMY OF SCIENCES, MOSCOW, RUSSIA
KLUWER ACADEMIC PUBLISHERS
DORDRECHT / BOSTON / LONDON
IMAGE 2
CONTENTS
PREFACE IX
CHAPTER 1. AGGREGATED PROBLEM AND BOUNDS
FOR AGGREGATION 1
§1. LINEAR PROGRAMMING AGGREGATION 1
1.1. DEFINITIONS AND PRELIMINARY RESULTS 2
1.2. A POSTERIORI BOUNDS 6
1.3. A PRIORI BOUNDS 8
1.4. SOME GENERALIZATIONS 10
1.4.1. A POSTERIORI BOUNDS 10
1.4.2. A PRIORI BOUNDS 17
1.5. ILLUSTRATIVE EXAMPLE AND NUMERICAL INDICATIONS - 19
§2. THE GENERALIZED TRANSPORTATION PROBLEM 25
2.1. THE AGGREGATED PROBLEM 26
2.2. THE ERROR BOUNDS 30
2.3. NUMERICAL INDICATIONS 35
§3. VARIABLE AGGREGATION IN NONLINEAR PROGRAMMING 38
§4. SHARPENING LOCALIZATION BY VALID INEQUALITIES IN
INTEGER PROGRAMMING 44
§5. THE GENERALIZED ASSIGNMENT PROBLEM 51
COMMENTS AND REFERENCES TO CHAPTER 1 58
CHAPTER 2. ITERATIVE AGGREGATION-DECOMPOSITION IN OPTIMIZATION PROBLEMS
61
§1. LINEAR AGGREGATION IN FINITE-DIMENSIONAL PROBLEMS 62
IMAGE 3
VI
§2. PROBLEMS WITH CONSTRAINTS OF SPECIAL STRUCTURE 72
§3. DECOMPOSITION OF THE MACROPROBLEM IN THE
BLOCK-SEPARABLE CASE 92
§4. ADAPTIVE CLUSTERING IN VARIABLE AGGREGATION 104
§5. AGGREGATION OF CONSTRAINTS 112
§6. AGGREGATION OF CONTROLS IN DYNAMIC PROBLEMS WITH MIXED CONSTRAINTS
121
§7. AGGREGATION OF STATE VARIABLES IN LINEAR-QUADRATIC PROBLEMS 129
§8. DISTRIBUTED PARAMETER SYSTEMS 135
§9. NUMERICAL INDICATIONS 147
COMMENTS AND REFERENCES TO CHAPTER 2 157
CHAPTER 3. CONSISTENT AGGREGATION IN PARAMETRIC OPTIMIZATION 163
§1. CONSISTENCY OF AGGREGATION WITH RESPECT TO PARAMETER
VARIATIONS 163
§2. PARAMETRIC LINEAR PROGRAMMING 166
2.1. THE BASE PROBLEM 167
2.2. AGGREGATION OF VARIABLES 170
2.3. CONSTRAINT REDUCTION 173
2.4. THE AGGREGATED PROBLEM IN THE STANDARD FORM
AND THE PROOF OF ITS CONSISTENCY 177
2.5. THE DEGENERATE CASE 187
2.6. VARIOUS FORMS OF THE BASE PROBLEM 189
2.7. AN EXAMPLE OF VARYING ONE ELEMENT IN THE CONSTRAINT MATRIX 198
§3. PARAMETRIC CONVEX PROGRAMMING 202
IMAGE 4
VII
3.1. VARYING PARAMETERS IN THE LINEAR PART OF CONSTRAINTS 202
3.2. PARAMETERS IN CONVEX CONSTRAINTS 217
§4. SPECIAL CLASSES OF PROBLEMS 233
4.1. STRONGER CONSISTENCY CONDITIONS. QUADRATIC PROGRAMMING 233
4.2. LINEAR-CONVEX PROBLEMS IN BANACH SPACES 245
4.3. OPTIMAL CONTROL OF LINEAR SYSTEMS UNDER TERMINAL CONSTRAINTS 256
4.4. WEAKER CONSISTENCY CONDITIONS. INTEGER LINEAR PROGRAMMING 264
4.4.1. A QUASI-CONSISTENCY THEOREM 272
4.4.2. USING THE CUTS OF THE PRIMAL ALGORITHM .. .. 278
COMMENTS AND REFERENCES TO CHAPTER 3 284
INDEX 289
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T19:18:06Z |
| institution | BVB |
| isbn | 1402075979 |
| language | English |
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| physical | xii, 291 p. graph. Darst. |
| publishDate | 2003 |
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| publisher | Kluwer Academic Publ. |
| record_format | marc |
| series | Applied optimization |
| series2 | Applied optimization |
| spelling | Litvinchev, Igor Verfasser aut Aggregation in large-scale optimization by Igor Litvinchev and Vladimir Tsurkov Dordrecht [u.a.] Kluwer Academic Publ. 2003 xii, 291 p. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Applied optimization 83 Includes bibliographical references and index Tsurkov, Vladimir I. Verfasser aut Applied optimization 83 (DE-604)BV010841718 83 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010510704&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Litvinchev, Igor Tsurkov, Vladimir I. Aggregation in large-scale optimization Applied optimization |
| title | Aggregation in large-scale optimization |
| title_auth | Aggregation in large-scale optimization |
| title_exact_search | Aggregation in large-scale optimization |
| title_full | Aggregation in large-scale optimization by Igor Litvinchev and Vladimir Tsurkov |
| title_fullStr | Aggregation in large-scale optimization by Igor Litvinchev and Vladimir Tsurkov |
| title_full_unstemmed | Aggregation in large-scale optimization by Igor Litvinchev and Vladimir Tsurkov |
| title_short | Aggregation in large-scale optimization |
| title_sort | aggregation in large scale optimization |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010510704&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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