In 1961, C. Zener, then Director of Science at Westinghouse Corpora- tion, 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 Mathe- matical 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 polymial, 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 Carnegie- Mellon University who joined forces with Zener in laying the rigorous mathematical foundations of optimizing generalized polymials. Interes- tingly, 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.
Product Identifiers
GTIN
9781461582878
UPC
9781461582878
eBay Product ID (ePID)
148731243
Product Key Features
Format
Paperback
Language
English
Subject
Mathematics
Type
Textbook
Dimensions
Item Height
234 mm
Weight
718g
Depth
24 mm
Height
234mm
Width
156mm
Item Weight
718 g
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