Download e-book for iPad: Advances in Geometric Programming by M. Avriel (auth.), Mordecai Avriel (eds.)

By M. Avriel (auth.), Mordecai Avriel (eds.)

ISBN-10: 1461582857

ISBN-13: 9781461582854

ISBN-10: 1461582873

ISBN-13: 9781461582878

In 1961, C. Zener, then Director of technological know-how at Westinghouse Corpora­ tion, and a member of the U. S. nationwide Academy of Sciences who has made very important contributions to physics and engineering, released a brief article within the complaints of the nationwide Academy of Sciences entitled" A Mathe­ matical reduction in Optimizing Engineering layout. " listed here Zener thought of the matter of discovering an optimum engineering layout that could frequently be expressed because the challenge of minimizing a numerical expense functionality, termed a "generalized polynomial," inclusive of a sum of phrases, the place each one time period is a made of a good consistent and the layout variables, raised to arbitrary powers. He saw that if the variety of phrases exceeds the variety of variables by way of one, the optimum values of the layout variables may be simply discovered by means of fixing a collection of linear equations. in addition, convinced invariances of the relative contribution of every time period to the entire expense should be deduced. The mathematical intricacies in Zener's procedure quickly raised the interest of R. J. Duffin, the celebrated mathematician from Carnegie­ Mellon college who joined forces with Zener in laying the rigorous mathematical foundations of optimizing generalized polynomials. Interes­ tingly, the research of optimality stipulations and houses of the optimum recommendations in such difficulties have been conducted by way of Duffin and Zener due to inequalities, instead of the extra universal strategy of the Kuhn-Tucker theory.

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Extra resources for Advances in Geometric Programming

Example text

2. 5. , q> 1). Then [(x) = {(I xf)l/p if x 2:0 +00 otherwise =-r t*(y) = {O if I y? 6. , q <0). Then g(X)={(Ixf)l/P -0 ,L... If x 2:0,x)s-0=-rg*(y) = h' -

In all cases, the symbol indicates the usual "inner product" function. ) 2. Problem Formulation and Examples Geometric programming provides a mechanism for formulating and studying in "separable" form many important (usually inseparable) optimization problems. The key to this mechanism is the exploitation of the linearities that are present in a given problem. Such linearities frequently appear as linear equations or linear inequalities, but they can also appear in much more subtle guises, such as matrices associated with nonlinearities.

Such linearities frequently appear as linear equations or linear inequalities, but they can also appear in rather subtle guises, such as matrices associated with nonlinearities. 1 can also be induced in any 42 E. L. Peterson constraint function of the same general type. We now use signomial optimization to illustrate the general procedure for doing so. 6. First, we make the following choices: i={1,2, ... '" no+1=ml~nl' np_l+1=mp~np=n, X £ column space of [a qr ], where [a qr ] is any n x m matrix.

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Advances in Geometric Programming by M. Avriel (auth.), Mordecai Avriel (eds.)


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