Other constraints might be obtained from formulas for
minimizing the difference between a product of variables
and a linear combination of same.
min PROD x[j] - SUM c[k]*x[k]
j in 1..n k in 1..n
set the derivative with respect to x[L] to 0:
PROD x[j] - c[L] = 0 for L in 1..n
j in 1..n - {L}
PROD x[j] = c[L] for L in 1..n
j in 1..n - {L}
multiplying n equations:
PROD x[j]**(n-1) = PROD c[j]
j in 1..n j in 1..n
PROD x[j] = PROD c[j]**(1/(n-1)
j in 1..n k in 1..n
dividing:
x[L] = c[L]**-1 * PROD c[j]**(1/(n-1))
j in 1..n
Note that I have assumed c> 0 and x> 0 .
--
Michael [email protected]
"Sorry but your password must contain an uppercase letter, a number,
a haiku, a gang sign, a heiroglyph, and the blood of a virgin."
-- someeecards
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