Generalized Convexity, Generalized Monotonicity: Recent Results:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Springer US
1998
|
| Schriftenreihe: | Nonconvex Optimization and Its Applications
27 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | A function is convex if its epigraph is convex. This geometrical structure has very strong implications in terms of continuity and differentiability. Separation theorems lead to optimality conditions and duality for convex problems. A function is quasiconvex if its lower level sets are convex. Here again, the geo metrical structure of the level sets implies some continuity and differentiability properties for quasiconvex functions. Optimality conditions and duality can be derived for optimization problems involving such functions as well. Over a period of about fifty years, quasiconvex and other generalized convex functions have been considered in a variety of fields including economies, man agement science, engineering, probability and applied sciences in accordance with the need of particular applications. During the last twenty-five years, an increase of research activities in this field has been witnessed. More recently generalized monotonicity of maps has been studied. It relates to generalized convexity off unctions as monotonicity relates to convexity. Generalized monotonicity plays a role in variational inequality problems, complementarity problems and more generally, in equilibrium prob lems |
| Beschreibung: | 1 Online-Ressource (XVI, 471 p) |
| ISBN: | 9781461333418 9781461333432 |
| ISSN: | 1571-568X |
| DOI: | 10.1007/978-1-4613-3341-8 |
Internformat
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Datensatz im Suchindex
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| any_adam_object | |
| author | Crouzeix, Jean-Pierre |
| author_facet | Crouzeix, Jean-Pierre |
| author_role | aut |
| author_sort | Crouzeix, Jean-Pierre |
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| building | Verbundindex |
| bvnumber | BV042420632 |
| 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 | 10.1007/978-1-4613-3341-8 |
| format | Electronic eBook |
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| isbn | 9781461333418 9781461333432 |
| issn | 1571-568X |
| language | English |
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| series2 | Nonconvex Optimization and Its Applications |
| spelling | Crouzeix, Jean-Pierre Verfasser aut Generalized Convexity, Generalized Monotonicity: Recent Results edited by Jean-Pierre Crouzeix, Juan-Enrique Martinez-Legaz, Michel Volle Boston, MA Springer US 1998 1 Online-Ressource (XVI, 471 p) txt rdacontent c rdamedia cr rdacarrier Nonconvex Optimization and Its Applications 27 1571-568X A function is convex if its epigraph is convex. This geometrical structure has very strong implications in terms of continuity and differentiability. Separation theorems lead to optimality conditions and duality for convex problems. A function is quasiconvex if its lower level sets are convex. Here again, the geo metrical structure of the level sets implies some continuity and differentiability properties for quasiconvex functions. Optimality conditions and duality can be derived for optimization problems involving such functions as well. Over a period of about fifty years, quasiconvex and other generalized convex functions have been considered in a variety of fields including economies, man agement science, engineering, probability and applied sciences in accordance with the need of particular applications. During the last twenty-five years, an increase of research activities in this field has been witnessed. More recently generalized monotonicity of maps has been studied. It relates to generalized convexity off unctions as monotonicity relates to convexity. Generalized monotonicity plays a role in variational inequality problems, complementarity problems and more generally, in equilibrium prob lems Mathematics Mathematical optimization Econometrics Economics Optimization Economic Theory Mathematik Wirtschaft Monotone Abbildung (DE-588)4204031-0 gnd rswk-swf Verallgemeinerte konvexe Funktion (DE-588)4262100-8 gnd rswk-swf 1\p (DE-588)1071861417 Konferenzschrift 1996 Marseille gnd-content Verallgemeinerte konvexe Funktion (DE-588)4262100-8 s 2\p DE-604 Monotone Abbildung (DE-588)4204031-0 s 3\p DE-604 Martinez-Legaz, Juan-Enrique Sonstige oth Volle, Michel Sonstige oth https://doi.org/10.1007/978-1-4613-3341-8 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Crouzeix, Jean-Pierre Generalized Convexity, Generalized Monotonicity: Recent Results Mathematics Mathematical optimization Econometrics Economics Optimization Economic Theory Mathematik Wirtschaft Monotone Abbildung (DE-588)4204031-0 gnd Verallgemeinerte konvexe Funktion (DE-588)4262100-8 gnd |
| subject_GND | (DE-588)4204031-0 (DE-588)4262100-8 (DE-588)1071861417 |
| title | Generalized Convexity, Generalized Monotonicity: Recent Results |
| title_auth | Generalized Convexity, Generalized Monotonicity: Recent Results |
| title_exact_search | Generalized Convexity, Generalized Monotonicity: Recent Results |
| title_full | Generalized Convexity, Generalized Monotonicity: Recent Results edited by Jean-Pierre Crouzeix, Juan-Enrique Martinez-Legaz, Michel Volle |
| title_fullStr | Generalized Convexity, Generalized Monotonicity: Recent Results edited by Jean-Pierre Crouzeix, Juan-Enrique Martinez-Legaz, Michel Volle |
| title_full_unstemmed | Generalized Convexity, Generalized Monotonicity: Recent Results edited by Jean-Pierre Crouzeix, Juan-Enrique Martinez-Legaz, Michel Volle |
| title_short | Generalized Convexity, Generalized Monotonicity: Recent Results |
| title_sort | generalized convexity generalized monotonicity recent results |
| topic | Mathematics Mathematical optimization Econometrics Economics Optimization Economic Theory Mathematik Wirtschaft Monotone Abbildung (DE-588)4204031-0 gnd Verallgemeinerte konvexe Funktion (DE-588)4262100-8 gnd |
| topic_facet | Mathematics Mathematical optimization Econometrics Economics Optimization Economic Theory Mathematik Wirtschaft Monotone Abbildung Verallgemeinerte konvexe Funktion Konferenzschrift 1996 Marseille |
| url | https://doi.org/10.1007/978-1-4613-3341-8 |
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