Vector Optimization: Theory, Applications, and Extensions
In vector optimization one investigates optimal elements such as min imal, strongly minimal, properly minimal or weakly minimal elements of a nonempty subset of a partially ordered linear space. The prob lem of determining at least one of these optimal elements, if they exist at all, is also calle...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
2004
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| Ausgabe: | 1st ed. 2004 |
| Schlagworte: | |
| Online-Zugang: | BTU01 Volltext |
| Zusammenfassung: | In vector optimization one investigates optimal elements such as min imal, strongly minimal, properly minimal or weakly minimal elements of a nonempty subset of a partially ordered linear space. The prob lem of determining at least one of these optimal elements, if they exist at all, is also called a vector optimization problem. Problems of this type can be found not only in mathematics but also in engineer ing and economics. Vector optimization problems arise, for exam ple, in functional analysis (the Hahn-Banach theorem, the lemma of Bishop-Phelps, Ekeland's variational principle), multiobjective pro gramming, multi-criteria decision making, statistics (Bayes solutions, theory of tests, minimal covariance matrices), approximation theory (location theory, simultaneous approximation, solution of boundary value problems) and cooperative game theory (cooperative n player differential games and, as a special case, optimal control problems). In the last decade vector optimization has been extended to problems with set-valued maps. This new field of research, called set optimiza tion, seems to have important applications to variational inequalities and optimization problems with multivalued data. The roots of vector optimization go back to F. Y. Edgeworth (1881) and V. Pareto (1896) who has already given the definition of the standard optimality concept in multiobjective optimization. But in mathematics this branch of optimization has started with the leg endary paper of H. W. Kuhn and A. W. Tucker (1951). Since about v Vl Preface the end of the 60's research is intensively made in vector optimization |
| Beschreibung: | 1 Online-Ressource (XIII, 465 p) |
| ISBN: | 9783540248286 |
| DOI: | 10.1007/978-3-540-24828-6 |
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| 520 | |a In vector optimization one investigates optimal elements such as min imal, strongly minimal, properly minimal or weakly minimal elements of a nonempty subset of a partially ordered linear space. The prob lem of determining at least one of these optimal elements, if they exist at all, is also called a vector optimization problem. Problems of this type can be found not only in mathematics but also in engineer ing and economics. Vector optimization problems arise, for exam ple, in functional analysis (the Hahn-Banach theorem, the lemma of Bishop-Phelps, Ekeland's variational principle), multiobjective pro gramming, multi-criteria decision making, statistics (Bayes solutions, theory of tests, minimal covariance matrices), approximation theory (location theory, simultaneous approximation, solution of boundary value problems) and cooperative game theory (cooperative n player differential games and, as a special case, optimal control problems). In the last decade vector optimization has been extended to problems with set-valued maps. This new field of research, called set optimiza tion, seems to have important applications to variational inequalities and optimization problems with multivalued data. The roots of vector optimization go back to F. Y. Edgeworth (1881) and V. Pareto (1896) who has already given the definition of the standard optimality concept in multiobjective optimization. But in mathematics this branch of optimization has started with the leg endary paper of H. W. Kuhn and A. W. Tucker (1951). Since about v Vl Preface the end of the 60's research is intensively made in vector optimization | ||
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| spelling | Jahn, Johannes Verfasser aut Vector Optimization Theory, Applications, and Extensions by Johannes Jahn 1st ed. 2004 Berlin, Heidelberg Springer Berlin Heidelberg 2004 1 Online-Ressource (XIII, 465 p) txt rdacontent c rdamedia cr rdacarrier In vector optimization one investigates optimal elements such as min imal, strongly minimal, properly minimal or weakly minimal elements of a nonempty subset of a partially ordered linear space. The prob lem of determining at least one of these optimal elements, if they exist at all, is also called a vector optimization problem. Problems of this type can be found not only in mathematics but also in engineer ing and economics. Vector optimization problems arise, for exam ple, in functional analysis (the Hahn-Banach theorem, the lemma of Bishop-Phelps, Ekeland's variational principle), multiobjective pro gramming, multi-criteria decision making, statistics (Bayes solutions, theory of tests, minimal covariance matrices), approximation theory (location theory, simultaneous approximation, solution of boundary value problems) and cooperative game theory (cooperative n player differential games and, as a special case, optimal control problems). In the last decade vector optimization has been extended to problems with set-valued maps. This new field of research, called set optimiza tion, seems to have important applications to variational inequalities and optimization problems with multivalued data. The roots of vector optimization go back to F. Y. Edgeworth (1881) and V. Pareto (1896) who has already given the definition of the standard optimality concept in multiobjective optimization. But in mathematics this branch of optimization has started with the leg endary paper of H. W. Kuhn and A. W. Tucker (1951). Since about v Vl Preface the end of the 60's research is intensively made in vector optimization Operations Research/Decision Theory Optimization Analysis Operations Research, Management Science Operations research Decision making Mathematical optimization Mathematical analysis Analysis (Mathematics) Management science Mehrkriterielle Optimierung (DE-588)4610682-0 gnd rswk-swf Mehrkriterielle Optimierung (DE-588)4610682-0 s DE-604 Erscheint auch als Druck-Ausgabe 9783642058288 Erscheint auch als Druck-Ausgabe 9783540206156 Erscheint auch als Druck-Ausgabe 9783662132821 https://doi.org/10.1007/978-3-540-24828-6 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Jahn, Johannes Vector Optimization Theory, Applications, and Extensions Operations Research/Decision Theory Optimization Analysis Operations Research, Management Science Operations research Decision making Mathematical optimization Mathematical analysis Analysis (Mathematics) Management science Mehrkriterielle Optimierung (DE-588)4610682-0 gnd |
| subject_GND | (DE-588)4610682-0 |
| title | Vector Optimization Theory, Applications, and Extensions |
| title_auth | Vector Optimization Theory, Applications, and Extensions |
| title_exact_search | Vector Optimization Theory, Applications, and Extensions |
| title_exact_search_txtP | Vector Optimization Theory, Applications, and Extensions |
| title_full | Vector Optimization Theory, Applications, and Extensions by Johannes Jahn |
| title_fullStr | Vector Optimization Theory, Applications, and Extensions by Johannes Jahn |
| title_full_unstemmed | Vector Optimization Theory, Applications, and Extensions by Johannes Jahn |
| title_short | Vector Optimization |
| title_sort | vector optimization theory applications and extensions |
| title_sub | Theory, Applications, and Extensions |
| topic | Operations Research/Decision Theory Optimization Analysis Operations Research, Management Science Operations research Decision making Mathematical optimization Mathematical analysis Analysis (Mathematics) Management science Mehrkriterielle Optimierung (DE-588)4610682-0 gnd |
| topic_facet | Operations Research/Decision Theory Optimization Analysis Operations Research, Management Science Operations research Decision making Mathematical optimization Mathematical analysis Analysis (Mathematics) Management science Mehrkriterielle Optimierung |
| url | https://doi.org/10.1007/978-3-540-24828-6 |
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