A Reformulation-Linearization Technique for Solving Discrete and Continuous Nonconvex Problems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Springer US
1999
|
| Schriftenreihe: | Nonconvex Optimization and Its Applications
31 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This book deals with the theory and applications of the Reformulation- Linearization/Convexification Technique (RL T) for solving nonconvex optimization problems. A unified treatment of discrete and continuous nonconvex programming problems is presented using this approach. In essence, the bridge between these two types of nonconvexities is made via a polynomial representation of discrete constraints. For example, the binariness on a 0-1 variable x . can be equivalently J expressed as the polynomial constraint x . (1-x . ) = 0. The motivation for this book is J J the role of tight linear/convex programming representations or relaxations in solving such discrete and continuous nonconvex programming problems. The principal thrust is to commence with a model that affords a useful representation and structure, and then to further strengthen this representation through automatic reformulation and constraint generation techniques. As mentioned above, the focal point of this book is the development and application of RL T for use as an automatic reformulation procedure, and also, to generate strong valid inequalities. The RLT operates in two phases. In the Reformulation Phase, certain types of additional implied polynomial constraints, that include the aforementioned constraints in the case of binary variables, are appended to the problem. The resulting problem is subsequently linearized, except that certain convex constraints are sometimes retained in XV particular special cases, in the Linearization/Convexijication Phase. This is done via the definition of suitable new variables to replace each distinct variable-product term. The higher dimensional representation yields a linear (or convex) programming relaxation |
| Beschreibung: | 1 Online-Ressource (XXIV, 518 p) |
| ISBN: | 9781475743883 9781441948083 |
| ISSN: | 1571-568X |
| DOI: | 10.1007/978-1-4757-4388-3 |
Internformat
MARC
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| 245 | 1 | 0 | |a A Reformulation-Linearization Technique for Solving Discrete and Continuous Nonconvex Problems |c by Hanif D. Sherali, Warren P. Adams |
| 264 | 1 | |a Boston, MA |b Springer US |c 1999 | |
| 300 | |a 1 Online-Ressource (XXIV, 518 p) | ||
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| 490 | 1 | |a Nonconvex Optimization and Its Applications |v 31 |x 1571-568X | |
| 500 | |a This book deals with the theory and applications of the Reformulation- Linearization/Convexification Technique (RL T) for solving nonconvex optimization problems. A unified treatment of discrete and continuous nonconvex programming problems is presented using this approach. In essence, the bridge between these two types of nonconvexities is made via a polynomial representation of discrete constraints. For example, the binariness on a 0-1 variable x . can be equivalently J expressed as the polynomial constraint x . (1-x . ) = 0. The motivation for this book is J J the role of tight linear/convex programming representations or relaxations in solving such discrete and continuous nonconvex programming problems. The principal thrust is to commence with a model that affords a useful representation and structure, and then to further strengthen this representation through automatic reformulation and constraint generation techniques. As mentioned above, the focal point of this book is the development and application of RL T for use as an automatic reformulation procedure, and also, to generate strong valid inequalities. The RLT operates in two phases. In the Reformulation Phase, certain types of additional implied polynomial constraints, that include the aforementioned constraints in the case of binary variables, are appended to the problem. The resulting problem is subsequently linearized, except that certain convex constraints are sometimes retained in XV particular special cases, in the Linearization/Convexijication Phase. This is done via the definition of suitable new variables to replace each distinct variable-product term. The higher dimensional representation yields a linear (or convex) programming relaxation | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Matrix theory | |
| 650 | 4 | |a Computer science / Mathematics | |
| 650 | 4 | |a Algorithms | |
| 650 | 4 | |a Combinatorics | |
| 650 | 4 | |a Mathematical optimization | |
| 650 | 4 | |a Optimization | |
| 650 | 4 | |a Computational Mathematics and Numerical Analysis | |
| 650 | 4 | |a Linear and Multilinear Algebras, Matrix Theory | |
| 650 | 4 | |a Informatik | |
| 650 | 4 | |a Mathematik | |
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Datensatz im Suchindex
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| any_adam_object | |
| author | Sherali, Hanif D. 1952- |
| author_GND | (DE-588)135768586 |
| author_facet | Sherali, Hanif D. 1952- |
| author_role | aut |
| author_sort | Sherali, Hanif D. 1952- |
| author_variant | h d s hd hds |
| building | Verbundindex |
| bvnumber | BV042421616 |
| classification_tum | MAT 000 |
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| dewey-full | 519.6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.6 |
| dewey-search | 519.6 |
| dewey-sort | 3519.6 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4757-4388-3 |
| format | Electronic eBook |
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| institution | BVB |
| isbn | 9781475743883 9781441948083 |
| issn | 1571-568X |
| language | English |
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| series | Nonconvex Optimization and Its Applications |
| series2 | Nonconvex Optimization and Its Applications |
| spelling | Sherali, Hanif D. 1952- Verfasser (DE-588)135768586 aut A Reformulation-Linearization Technique for Solving Discrete and Continuous Nonconvex Problems by Hanif D. Sherali, Warren P. Adams Boston, MA Springer US 1999 1 Online-Ressource (XXIV, 518 p) txt rdacontent c rdamedia cr rdacarrier Nonconvex Optimization and Its Applications 31 1571-568X This book deals with the theory and applications of the Reformulation- Linearization/Convexification Technique (RL T) for solving nonconvex optimization problems. A unified treatment of discrete and continuous nonconvex programming problems is presented using this approach. In essence, the bridge between these two types of nonconvexities is made via a polynomial representation of discrete constraints. For example, the binariness on a 0-1 variable x . can be equivalently J expressed as the polynomial constraint x . (1-x . ) = 0. The motivation for this book is J J the role of tight linear/convex programming representations or relaxations in solving such discrete and continuous nonconvex programming problems. The principal thrust is to commence with a model that affords a useful representation and structure, and then to further strengthen this representation through automatic reformulation and constraint generation techniques. As mentioned above, the focal point of this book is the development and application of RL T for use as an automatic reformulation procedure, and also, to generate strong valid inequalities. The RLT operates in two phases. In the Reformulation Phase, certain types of additional implied polynomial constraints, that include the aforementioned constraints in the case of binary variables, are appended to the problem. The resulting problem is subsequently linearized, except that certain convex constraints are sometimes retained in XV particular special cases, in the Linearization/Convexijication Phase. This is done via the definition of suitable new variables to replace each distinct variable-product term. The higher dimensional representation yields a linear (or convex) programming relaxation Mathematics Matrix theory Computer science / Mathematics Algorithms Combinatorics Mathematical optimization Optimization Computational Mathematics and Numerical Analysis Linear and Multilinear Algebras, Matrix Theory Informatik Mathematik Nichtkonvexe Optimierung (DE-588)4309215-9 gnd rswk-swf Linearisierung (DE-588)4199872-8 gnd rswk-swf Nichtkonvexe Optimierung (DE-588)4309215-9 s Linearisierung (DE-588)4199872-8 s 1\p DE-604 Adams, Warren P. Sonstige oth Nonconvex Optimization and Its Applications 31 (DE-604)BV036654736 31 https://doi.org/10.1007/978-1-4757-4388-3 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Sherali, Hanif D. 1952- A Reformulation-Linearization Technique for Solving Discrete and Continuous Nonconvex Problems Nonconvex Optimization and Its Applications Mathematics Matrix theory Computer science / Mathematics Algorithms Combinatorics Mathematical optimization Optimization Computational Mathematics and Numerical Analysis Linear and Multilinear Algebras, Matrix Theory Informatik Mathematik Nichtkonvexe Optimierung (DE-588)4309215-9 gnd Linearisierung (DE-588)4199872-8 gnd |
| subject_GND | (DE-588)4309215-9 (DE-588)4199872-8 |
| title | A Reformulation-Linearization Technique for Solving Discrete and Continuous Nonconvex Problems |
| title_auth | A Reformulation-Linearization Technique for Solving Discrete and Continuous Nonconvex Problems |
| title_exact_search | A Reformulation-Linearization Technique for Solving Discrete and Continuous Nonconvex Problems |
| title_full | A Reformulation-Linearization Technique for Solving Discrete and Continuous Nonconvex Problems by Hanif D. Sherali, Warren P. Adams |
| title_fullStr | A Reformulation-Linearization Technique for Solving Discrete and Continuous Nonconvex Problems by Hanif D. Sherali, Warren P. Adams |
| title_full_unstemmed | A Reformulation-Linearization Technique for Solving Discrete and Continuous Nonconvex Problems by Hanif D. Sherali, Warren P. Adams |
| title_short | A Reformulation-Linearization Technique for Solving Discrete and Continuous Nonconvex Problems |
| title_sort | a reformulation linearization technique for solving discrete and continuous nonconvex problems |
| topic | Mathematics Matrix theory Computer science / Mathematics Algorithms Combinatorics Mathematical optimization Optimization Computational Mathematics and Numerical Analysis Linear and Multilinear Algebras, Matrix Theory Informatik Mathematik Nichtkonvexe Optimierung (DE-588)4309215-9 gnd Linearisierung (DE-588)4199872-8 gnd |
| topic_facet | Mathematics Matrix theory Computer science / Mathematics Algorithms Combinatorics Mathematical optimization Optimization Computational Mathematics and Numerical Analysis Linear and Multilinear Algebras, Matrix Theory Informatik Mathematik Nichtkonvexe Optimierung Linearisierung |
| url | https://doi.org/10.1007/978-1-4757-4388-3 |
| volume_link | (DE-604)BV036654736 |
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