[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]
Re: [Help-glpk] Non linear constraint
|
From: |
Michael Hennebry |
|
Subject: |
Re: [Help-glpk] Non linear constraint |
|
Date: |
Mon, 9 Nov 2015 17:32:37 -0600 (CST) |
|
User-agent: |
Alpine 1.00 (DEB 882 2007-12-20) |
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 address@hidden
"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