Advances in Geometric Programming:
Gespeichert in:
| Weitere Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Springer US
1980
|
| Schriftenreihe: | Mathematical Concepts and Methods in Science and Engineering
21 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | In 1961, C. Zener, then Director of Science at Westinghouse Corporation, and a member of the U. S. National Academy of Sciences who has made important contributions to physics and engineering, published a short article in the Proceedings of the National Academy of Sciences entitled" A Mathematical Aid in Optimizing Engineering Design. " In this article Zener considered the problem of finding an optimal engineering design that can often be expressed as the problem of minimizing a numerical cost function, termed a "generalized polynomial," consisting of a sum of terms, where each term is a product of a positive constant and the design variables, raised to arbitrary powers. He observed that if the number of terms exceeds the number of variables by one, the optimal values of the design variables can be easily found by solving a set of linear equations. Furthermore, certain invariances of the relative contribution of each term to the total cost can be deduced. The mathematical intricacies in Zener's method soon raised the curiosity of R. J. Duffin, the distinguished mathematician from CarnegieMellon University who joined forces with Zener in laying the rigorous mathematical foundations of optimizing generalized polynomials. Interestingly, the investigation of optimality conditions and properties of the optimal solutions in such problems were carried out by Duffin and Zener with the aid of inequalities, rather than the more common approach of the Kuhn-Tucker theory |
| Beschreibung: | 1 Online-Ressource (X, 460 p) |
| ISBN: | 9781461582854 9781461582878 |
| DOI: | 10.1007/978-1-4615-8285-4 |
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| 490 | 1 | |a Mathematical Concepts and Methods in Science and Engineering |v 21 | |
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| id | DE-604.BV042420961 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:08Z |
| institution | BVB |
| isbn | 9781461582854 9781461582878 |
| language | English |
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| physical | 1 Online-Ressource (X, 460 p) |
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| publishDate | 1980 |
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| publisher | Springer US |
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| series | Mathematical Concepts and Methods in Science and Engineering |
| series2 | Mathematical Concepts and Methods in Science and Engineering |
| spelling | Advances in Geometric Programming edited by Mordecai Avriel Boston, MA Springer US 1980 1 Online-Ressource (X, 460 p) txt rdacontent c rdamedia cr rdacarrier Mathematical Concepts and Methods in Science and Engineering 21 In 1961, C. Zener, then Director of Science at Westinghouse Corporation, and a member of the U. S. National Academy of Sciences who has made important contributions to physics and engineering, published a short article in the Proceedings of the National Academy of Sciences entitled" A Mathematical Aid in Optimizing Engineering Design. " In this article Zener considered the problem of finding an optimal engineering design that can often be expressed as the problem of minimizing a numerical cost function, termed a "generalized polynomial," consisting of a sum of terms, where each term is a product of a positive constant and the design variables, raised to arbitrary powers. He observed that if the number of terms exceeds the number of variables by one, the optimal values of the design variables can be easily found by solving a set of linear equations. Furthermore, certain invariances of the relative contribution of each term to the total cost can be deduced. The mathematical intricacies in Zener's method soon raised the curiosity of R. J. Duffin, the distinguished mathematician from CarnegieMellon University who joined forces with Zener in laying the rigorous mathematical foundations of optimizing generalized polynomials. Interestingly, the investigation of optimality conditions and properties of the optimal solutions in such problems were carried out by Duffin and Zener with the aid of inequalities, rather than the more common approach of the Kuhn-Tucker theory Mathematics Discrete groups Convex and Discrete Geometry Mathematik Avriel, Mordekhai (DE-588)127119523 edt Mathematical Concepts and Methods in Science and Engineering 21 (DE-604)BV000001144 21 https://doi.org/10.1007/978-1-4615-8285-4 Verlag Volltext |
| spellingShingle | Advances in Geometric Programming Mathematical Concepts and Methods in Science and Engineering Mathematics Discrete groups Convex and Discrete Geometry Mathematik |
| title | Advances in Geometric Programming |
| title_auth | Advances in Geometric Programming |
| title_exact_search | Advances in Geometric Programming |
| title_full | Advances in Geometric Programming edited by Mordecai Avriel |
| title_fullStr | Advances in Geometric Programming edited by Mordecai Avriel |
| title_full_unstemmed | Advances in Geometric Programming edited by Mordecai Avriel |
| title_short | Advances in Geometric Programming |
| title_sort | advances in geometric programming |
| topic | Mathematics Discrete groups Convex and Discrete Geometry Mathematik |
| topic_facet | Mathematics Discrete groups Convex and Discrete Geometry Mathematik |
| url | https://doi.org/10.1007/978-1-4615-8285-4 |
| volume_link | (DE-604)BV000001144 |
| work_keys_str_mv | AT avrielmordekhai advancesingeometricprogramming |