level 1
赵小小背
楼主
各位老师好，我用FindMaximum求函数最大值的时候遇到了奇怪的状况，求出的最大值并不是真正的最大值，具体如下：
ClearAll["Global`*"]
w1 = 15
w2 = 18
p = 25
c = 2
\[Gamma]0 = 0.4
\[Gamma] = 0.6
\[Theta] = 1
\[Mu] = 200
\[Sigma] = 30
b = 45
k = 5
f[z_] = PDF[NormalDistribution[\[Mu], \[Sigma]], z]
GA[x_] = CDF[UniformDistribution[{0, b}], x]
\[CapitalPi]1 = \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(Q/\((\[Gamma]0*\((1 -
GA[p])\))\)\)]\(\((p*\[Gamma]0*\((1 - GA[p])\)*z - w1*Q -
c*R)\) f[z] \[DifferentialD]z\)\) + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Q/\((\[Gamma]0*\((1 -
GA[p])\))\)\), \(\((Q +
R)\)/\((\[Gamma]0*\((1 - GA[p])\))\)\)]\(\((p*\[Gamma]0*\((1 -
GA[p])\)*z - w1*Q -
w2*\((\[Gamma]0*\((1 - GA[p])\)*z - Q)\) - c*R)\) f[
z] \[DifferentialD]z\)\) + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(\((Q +
R)\)/\((\[Gamma]0*\((1 -
GA[p])\))\)\), \(+\[Infinity]\)]\(\((p*\((Q + R)\) - w1*Q -
w2*R - c*R)\) f[z] \[DifferentialD]z\)\)
FindMaximum[{\[CapitalPi]1, Q >= 0 && R >= 0}, {Q, R}]
这是求解过程，然后求出来的结果为：{258.52, {Q -> 28.5648, R -> 1.54233*10^-9}}
我用Q=33，R=6代入原式，得到的结果是310.435，代码如下：
ClearAll["Global`*"]
w1 = 15
w2 = 18
p = 25
c = 2
\[Gamma]0 = 0.4
\[Gamma] = 0.6
\[Theta] = 1
\[Mu] = 200
\[Sigma] = 30
b = 45
k = 5
Q = 33
R = 6
f[z_] = PDF[NormalDistribution[\[Mu], \[Sigma]], z]
GA[x_] = CDF[UniformDistribution[{0, b}], x]
\[CapitalPi]1 = \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(Q/\((\[Gamma]0*\((1 -
GA[p])\))\)\)]\(\((p*\[Gamma]0*\((1 - GA[p])\)*z - w1*Q -
c*R)\) f[z] \[DifferentialD]z\)\) + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Q/\((\[Gamma]0*\((1 -
GA[p])\))\)\), \(\((Q +
R)\)/\((\[Gamma]0*\((1 - GA[p])\))\)\)]\(\((p*\[Gamma]0*\((1 -
GA[p])\)*z - w1*Q -
w2*\((\[Gamma]0*\((1 - GA[p])\)*z - Q)\) - c*R)\) f[
z] \[DifferentialD]z\)\) + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(\((Q +
R)\)/\((\[Gamma]0*\((1 -
GA[p])\))\)\), \(+\[Infinity]\)]\(\((p*\((Q + R)\) - w1*Q -
w2*R - c*R)\) f[z] \[DifferentialD]z\)\)
已经核对过两个式子是一样的，这就说明之前求出的并不是最大值呀，求帮助。
2018年03月07日 12点03分
1
ClearAll["Global`*"]
w1 = 15
w2 = 18
p = 25
c = 2
\[Gamma]0 = 0.4
\[Gamma] = 0.6
\[Theta] = 1
\[Mu] = 200
\[Sigma] = 30
b = 45
k = 5
f[z_] = PDF[NormalDistribution[\[Mu], \[Sigma]], z]
GA[x_] = CDF[UniformDistribution[{0, b}], x]
\[CapitalPi]1 = \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(Q/\((\[Gamma]0*\((1 -
GA[p])\))\)\)]\(\((p*\[Gamma]0*\((1 - GA[p])\)*z - w1*Q -
c*R)\) f[z] \[DifferentialD]z\)\) + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Q/\((\[Gamma]0*\((1 -
GA[p])\))\)\), \(\((Q +
R)\)/\((\[Gamma]0*\((1 - GA[p])\))\)\)]\(\((p*\[Gamma]0*\((1 -
GA[p])\)*z - w1*Q -
w2*\((\[Gamma]0*\((1 - GA[p])\)*z - Q)\) - c*R)\) f[
z] \[DifferentialD]z\)\) + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(\((Q +
R)\)/\((\[Gamma]0*\((1 -
GA[p])\))\)\), \(+\[Infinity]\)]\(\((p*\((Q + R)\) - w1*Q -
w2*R - c*R)\) f[z] \[DifferentialD]z\)\)
FindMaximum[{\[CapitalPi]1, Q >= 0 && R >= 0}, {Q, R}]
这是求解过程，然后求出来的结果为：{258.52, {Q -> 28.5648, R -> 1.54233*10^-9}}
我用Q=33，R=6代入原式，得到的结果是310.435，代码如下：
ClearAll["Global`*"]
w1 = 15
w2 = 18
p = 25
c = 2
\[Gamma]0 = 0.4
\[Gamma] = 0.6
\[Theta] = 1
\[Mu] = 200
\[Sigma] = 30
b = 45
k = 5
Q = 33
R = 6
f[z_] = PDF[NormalDistribution[\[Mu], \[Sigma]], z]
GA[x_] = CDF[UniformDistribution[{0, b}], x]
\[CapitalPi]1 = \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(Q/\((\[Gamma]0*\((1 -
GA[p])\))\)\)]\(\((p*\[Gamma]0*\((1 - GA[p])\)*z - w1*Q -
c*R)\) f[z] \[DifferentialD]z\)\) + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(Q/\((\[Gamma]0*\((1 -
GA[p])\))\)\), \(\((Q +
R)\)/\((\[Gamma]0*\((1 - GA[p])\))\)\)]\(\((p*\[Gamma]0*\((1 -
GA[p])\)*z - w1*Q -
w2*\((\[Gamma]0*\((1 - GA[p])\)*z - Q)\) - c*R)\) f[
z] \[DifferentialD]z\)\) + \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(\((Q +
R)\)/\((\[Gamma]0*\((1 -
GA[p])\))\)\), \(+\[Infinity]\)]\(\((p*\((Q + R)\) - w1*Q -
w2*R - c*R)\) f[z] \[DifferentialD]z\)\)
已经核对过两个式子是一样的，这就说明之前求出的并不是最大值呀，求帮助。
