Infinite Programming: Proceedings of an International Symposium on Infinite Dimensional Linear Programming Churchill College, Cambridge, United Kingdom, September 7–10, 1984
Infinite programming may be defined as the study of mathematical programming problems in which the number of variables and the number of constraints are both possibly infinite. Many optimization problems in engineering, operations research, and economics have natural formul- ions as infinite program...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
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Berlin, Heidelberg
Springer Berlin Heidelberg
1985
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| Ausgabe: | 1st ed. 1985 |
| Schriftenreihe: | Lecture Notes in Economics and Mathematical Systems
259 |
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| Online-Zugang: | BTU01 Volltext |
| Zusammenfassung: | Infinite programming may be defined as the study of mathematical programming problems in which the number of variables and the number of constraints are both possibly infinite. Many optimization problems in engineering, operations research, and economics have natural formul- ions as infinite programs. For example, the problem of Chebyshev approximation can be posed as a linear program with an infinite number of constraints. Formally, given continuous functions f,gl,g2, ••• ,gn on the interval [a,b], we can find the linear combination of the functions gl,g2, ... ,gn which is the best uniform approximation to f by choosing real numbers a,xl,x2, •.. ,x to n minimize a t€ [a,b]. This is an example of a semi-infinite program; the number of variables is finite and the number of constraints is infinite. An example of an infinite program in which the number of constraints and the number of variables are both infinite, is the well-known continuous linear program which can be formulated as follows. T minimize ~ c(t)Tx(t)dt t b(t) , subject to Bx(t) + fo Kx(s)ds x(t) .. 0, t € [0, T] • If x is regarded as a member of some infinite-dimensional vector space of functions, then this problem is a linear program posed over that space. Observe that if the constraint equations are differentiated, then this problem takes the form of a linear optimal control problem with state IV variable inequality constraints |
| Beschreibung: | 1 Online-Ressource (XIV, 248 p) |
| ISBN: | 9783642465642 |
| DOI: | 10.1007/978-3-642-46564-2 |
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| 245 | 1 | 0 | |a Infinite Programming |b Proceedings of an International Symposium on Infinite Dimensional Linear Programming Churchill College, Cambridge, United Kingdom, September 7–10, 1984 |c edited by Edward J. Anderson, Andrew B. Philpott |
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| 520 | |a Infinite programming may be defined as the study of mathematical programming problems in which the number of variables and the number of constraints are both possibly infinite. Many optimization problems in engineering, operations research, and economics have natural formul- ions as infinite programs. For example, the problem of Chebyshev approximation can be posed as a linear program with an infinite number of constraints. Formally, given continuous functions f,gl,g2, ••• ,gn on the interval [a,b], we can find the linear combination of the functions gl,g2, ... ,gn which is the best uniform approximation to f by choosing real numbers a,xl,x2, •.. ,x to n minimize a t€ [a,b]. This is an example of a semi-infinite program; the number of variables is finite and the number of constraints is infinite. An example of an infinite program in which the number of constraints and the number of variables are both infinite, is the well-known continuous linear program which can be formulated as follows. T minimize ~ c(t)Tx(t)dt t b(t) , subject to Bx(t) + fo Kx(s)ds x(t) .. 0, t € [0, T] • If x is regarded as a member of some infinite-dimensional vector space of functions, then this problem is a linear program posed over that space. Observe that if the constraint equations are differentiated, then this problem takes the form of a linear optimal control problem with state IV variable inequality constraints | ||
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| discipline | Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Mathematik Wirtschaftswissenschaften |
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| edition | 1st ed. 1985 |
| format | Electronic eBook |
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| spelling | Infinite Programming Proceedings of an International Symposium on Infinite Dimensional Linear Programming Churchill College, Cambridge, United Kingdom, September 7–10, 1984 edited by Edward J. Anderson, Andrew B. Philpott 1st ed. 1985 Berlin, Heidelberg Springer Berlin Heidelberg 1985 1 Online-Ressource (XIV, 248 p) txt rdacontent c rdamedia cr rdacarrier Lecture Notes in Economics and Mathematical Systems 259 Infinite programming may be defined as the study of mathematical programming problems in which the number of variables and the number of constraints are both possibly infinite. Many optimization problems in engineering, operations research, and economics have natural formul- ions as infinite programs. For example, the problem of Chebyshev approximation can be posed as a linear program with an infinite number of constraints. Formally, given continuous functions f,gl,g2, ••• ,gn on the interval [a,b], we can find the linear combination of the functions gl,g2, ... ,gn which is the best uniform approximation to f by choosing real numbers a,xl,x2, •.. ,x to n minimize a t€ [a,b]. This is an example of a semi-infinite program; the number of variables is finite and the number of constraints is infinite. An example of an infinite program in which the number of constraints and the number of variables are both infinite, is the well-known continuous linear program which can be formulated as follows. T minimize ~ c(t)Tx(t)dt t b(t) , subject to Bx(t) + fo Kx(s)ds x(t) .. 0, t € [0, T] • If x is regarded as a member of some infinite-dimensional vector space of functions, then this problem is a linear program posed over that space. Observe that if the constraint equations are differentiated, then this problem takes the form of a linear optimal control problem with state IV variable inequality constraints Economic Theory/Quantitative Economics/Mathematical Methods Economic theory Optimierung (DE-588)4043664-0 gnd rswk-swf Unendlichdimensionaler Raum (DE-588)4207852-0 gnd rswk-swf Unendlichdimensionales System (DE-588)4207956-1 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 1984 Cambridge gnd-content (DE-588)1071861417 Konferenzschrift gnd-content (DE-588)4143413-4 Aufsatzsammlung gnd-content Optimierung (DE-588)4043664-0 s Unendlichdimensionales System (DE-588)4207956-1 s DE-604 Unendlichdimensionaler Raum (DE-588)4207852-0 s Anderson, Edward J. edt Philpott, Andrew B. edt Erscheint auch als Druck-Ausgabe 9783540159964 Erscheint auch als Druck-Ausgabe 9783642465659 https://doi.org/10.1007/978-3-642-46564-2 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Infinite Programming Proceedings of an International Symposium on Infinite Dimensional Linear Programming Churchill College, Cambridge, United Kingdom, September 7–10, 1984 Economic Theory/Quantitative Economics/Mathematical Methods Economic theory Optimierung (DE-588)4043664-0 gnd Unendlichdimensionaler Raum (DE-588)4207852-0 gnd Unendlichdimensionales System (DE-588)4207956-1 gnd |
| subject_GND | (DE-588)4043664-0 (DE-588)4207852-0 (DE-588)4207956-1 (DE-588)1071861417 (DE-588)4143413-4 |
| title | Infinite Programming Proceedings of an International Symposium on Infinite Dimensional Linear Programming Churchill College, Cambridge, United Kingdom, September 7–10, 1984 |
| title_auth | Infinite Programming Proceedings of an International Symposium on Infinite Dimensional Linear Programming Churchill College, Cambridge, United Kingdom, September 7–10, 1984 |
| title_exact_search | Infinite Programming Proceedings of an International Symposium on Infinite Dimensional Linear Programming Churchill College, Cambridge, United Kingdom, September 7–10, 1984 |
| title_exact_search_txtP | Infinite Programming Proceedings of an International Symposium on Infinite Dimensional Linear Programming Churchill College, Cambridge, United Kingdom, September 7–10, 1984 |
| title_full | Infinite Programming Proceedings of an International Symposium on Infinite Dimensional Linear Programming Churchill College, Cambridge, United Kingdom, September 7–10, 1984 edited by Edward J. Anderson, Andrew B. Philpott |
| title_fullStr | Infinite Programming Proceedings of an International Symposium on Infinite Dimensional Linear Programming Churchill College, Cambridge, United Kingdom, September 7–10, 1984 edited by Edward J. Anderson, Andrew B. Philpott |
| title_full_unstemmed | Infinite Programming Proceedings of an International Symposium on Infinite Dimensional Linear Programming Churchill College, Cambridge, United Kingdom, September 7–10, 1984 edited by Edward J. Anderson, Andrew B. Philpott |
| title_short | Infinite Programming |
| title_sort | infinite programming proceedings of an international symposium on infinite dimensional linear programming churchill college cambridge united kingdom september 7 10 1984 |
| title_sub | Proceedings of an International Symposium on Infinite Dimensional Linear Programming Churchill College, Cambridge, United Kingdom, September 7–10, 1984 |
| topic | Economic Theory/Quantitative Economics/Mathematical Methods Economic theory Optimierung (DE-588)4043664-0 gnd Unendlichdimensionaler Raum (DE-588)4207852-0 gnd Unendlichdimensionales System (DE-588)4207956-1 gnd |
| topic_facet | Economic Theory/Quantitative Economics/Mathematical Methods Economic theory Optimierung Unendlichdimensionaler Raum Unendlichdimensionales System Konferenzschrift 1984 Cambridge Konferenzschrift Aufsatzsammlung |
| url | https://doi.org/10.1007/978-3-642-46564-2 |
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