m******t
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. | d*****1
发帖数: 1837 | 2 the model can be solved as dynamic optimization, such as
min |s1(M) - k1| + |s2(M) - k2|
\dot{s}_0 = f(x)
\dot{s}_1 = x*f(x)
\dot{s}_2 = x^2*f(x)
s_0(0) = 0
s_0(M) = 1
s_1(0) = 0
s_2(0) = 0 | m******t
发帖数: 273 | 3 Would you please explain what is dot{s}_0 ?
What are
s_0(0) = 0
s_0(M) = 1
s_1(0) = 0
s_2(0) = 0
?
Thanks !
【在 d*****1 的大作中提到】
: the model can be solved as dynamic optimization, such as
: min |s1(M) - k1| + |s2(M) - k2|
: \dot{s}_0 = f(x)
: \dot{s}_1 = x*f(x)
: \dot{s}_2 = x^2*f(x)
: s_0(0) = 0
: s_0(M) = 1
: s_1(0) = 0
: s_2(0) = 0
| d*****1
发帖数: 1837 | | m******t
发帖数: 273 | 5 I am not familar with dynamic optimization.
Why ODE needs to be used here ?
Thanks
【在 d*****1 的大作中提到】
: the model can be solved as dynamic optimization, such as
: min |s1(M) - k1| + |s2(M) - k2|
: \dot{s}_0 = f(x)
: \dot{s}_1 = x*f(x)
: \dot{s}_2 = x^2*f(x)
: s_0(0) = 0
: s_0(M) = 1
: s_1(0) = 0
: s_2(0) = 0
|
|
