ISSN:
1573-2878
Keywords:
Stochastic zero-degree geometric programs
;
Mellin transform of dual function
;
lognormal distribution of objective function
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract The Mellin transform is used to encode randomness in the constraint and objective function coefficients using the substituted dual function. This enables one to obtain statistical moments and the probability distribution of the optimal objective valueZ*. Advantage is taken of the form of the dual function and the limiting property of the lognormal distribution to prove that the probability distribution ofZ* approximates the lognormal distribution, independent of the distribution of the parameters. This is of importance because those probability distributions are seldom known; even if they are, a derivation of the distribution ofZ* is apt to be elusive. Further, the larger the number of stochastic parameters in the geometric program, the more closely, in general, does the distribution ofZ* approximate the lognormal distribution. Illustrative examples are provided.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00932305
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