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发帖数: 273 | 1 【 以下文字转载自 Statistics 讨论区 】
发信人: myregmit (myregmit), 信区: Statistics
标 题: solve an optimization model with integral as constraints
发信站: BBS 未名空间站 (Wed Mar 19 22:21:44 2014, 美东)
I need to solve a mathematical optimization model with integral as
constraints.
Min. | s1 - k1 | + | s2- k2 |
s.t.
integral_from_0_to_M of f(x) = 1
s1 = integral_from_0_to_M of x * f(x)
s2 = integral_from_0_to_M of x^2 * f(x)
M, k1 and k2 are positive numbers
f(x) is a probability density function of x with arguments of
(alpha, beta, 0, M)
f(x) = G * (x * beta)^(alpha -1) * e^(-x * beta)
G = alpha * beta / [( gamma(alpha, 0) - gamma(alpha, M) + e^(-M*beta
) * beat^(1-alpha) * M^alpha]
Decision variables:
alpha > 0, beta > 0
Any help would be appreciated. |
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