- #1
and [/ code] tags like
[code]
this
a = 1/4; b = 4044 + 4.0/9; c = 66 + 2.0/3; d =
15.0/1000; x0 = 0.0; x3 = 5.0; n = 3; K = 9.0; c2 = 0.1; \[Alpha] = \
0.25; p2 = 35.0; c1 = 25.0; i2 = 0.04; i1 = 0.05; \[Theta] = 0.03;
R[x_, y_] =
Integrate[
a*(E^(-d*t)*(E^(d*t)*(b - c*t) + E^(d*y)*(-b + c*y)))^2, {t, x,
y}];
F[x_, y_] =
Integrate[
a*(E^(d*t)*(E^(d*t)*(b - c*t) + E^(d*y)*(-b + c*y)))^2, {t,
y*(1 - \[Alpha]) + x*\[Alpha], y}];
H[x_, y_] =
0.5*Integrate[
Integrate[
E^(d*t)*(6 +
t)*((E^(d*t)*(b - c*t) + E^(d*y)*(-b + c*y))^2)^0.5, {t, x,
t}], {t, x, y + x*\[Alpha] - y*\[Alpha]}];
NMinimize[{n*K + c2*(R[x0, x1] + R[x1, x2] + R[x2, x3]) +
c1*i1*(F[x0, x1] + F[x1, x2] + F[x2, x3]) -
p2*i2*(H[x0, x1] + H[x1, x2] + H[x2, x3]),
x0 <= x1 && x1 <= x2 && x2 <= x3}, {x0, x1, x2, x3}]
Integrate[f[t], {t, x, t}]
R[x_?NumericQ, y_?NumericQ] :=
NIntegrate[
a*(E^(-d*t)*(E^(d*t)*(b - c*t) + E^(d*y)*(-b + c*y)))^2, {t, x, y} //
Evaluate]
F[x_?NumericQ, y_?NumericQ] :=
NIntegrate[
a*(E^(d*t)*(E^(d*t)*(b - c*t) + E^(d*y)*(-b + c*y)))^2, {t,
y*(1 - \[Alpha]) + x*\[Alpha], y} // Evaluate]
H[x_?NumericQ, y_?NumericQ] :=
0.5*NIntegrate[
E^(d*t)*(6 +
t)*((E^(d*t)*(b - c*t) + E^(d*y)*(-b + c*y))^2)^0.5, {\[Tau],
x, y + x*\[Alpha] - y*\[Alpha]}, {t, x, \[Tau]}];
FindMinimum[{n*K + c2*(R[x0, x1] + R[x1, x2] + R[x2, x3]) +
c1*i1*(F[x0, x1] + F[x1, x2] + F[x2, x3]) -
p2*i2*(H[x0, x1] + H[x1, x2] + H[x2, x3]),
x0 <= x1 <= x2 <= x3}, {{x1, 1}, {x2, 3}}]
There could be several reasons for this. It could be due to the complexity of the objective function, the number of variables being optimized, or the desired precision level. It could also be due to a lack of memory or processing power on your computer.
There are a few things you can try to speed up your program. First, you can try using the "Method" option in the NMinimize function to specify a more efficient optimization algorithm. You can also try simplifying your objective function or reducing the number of variables being optimized. Additionally, upgrading your computer's hardware or using a cloud computing service can also help improve performance.
Yes, you can parallelize your NMinimize program to utilize multiple processor cores and speed up the computation. This can be done using the "Parallelization" option in the NMinimize function and specifying the number of parallel kernels to use. However, not all optimization algorithms support parallelization, so you may need to experiment with different methods to find the best one for your specific problem.
Yes, you can use the "EvaluationMonitor" option in the NMinimize function to track the progress of your optimization. This will allow you to see the current values of the variables being optimized and the corresponding objective function value at each iteration. You can also use the "StepMonitor" option to view the optimization steps being taken.
If your program keeps failing, it could be due to numerical instabilities in the objective function or constraints. In this case, you may need to adjust the precision level or try using a different optimization algorithm. If the results are incorrect, you should carefully check your objective function and constraints to ensure they are correctly defined. You can also try using the "EvaluationMonitor" and "StepMonitor" options to identify any potential issues with your optimization process.