I need to find the global minimum of the following function:
eq=(sig1tr/Sqrt[3] + sig2tr/Sqrt[3] + sig3tr/Sqrt[3] - xi)^2/(
3 K) + ((Sqrt[2/3] sig1tr - sig2tr/Sqrt[6] - sig3tr/Sqrt[6] -
Sqrt[2] (A - C E^(Sqrt[3] B xi)) Cos[beta])^2 + (sig2tr/Sqrt[2] -
sig3tr/Sqrt[2] - Sqrt[2] (A - C E^(Sqrt[3] B xi)) Sin[beta])^2)/(
2 G)
Where G>0, K>0, A>0,C>0,B>0, sigtr1,sigtr2 and sigtr3
are real constants. Aditionaly sigtr1>sigtr2>sigtr3
. I need to find the variables values ofxi and beta
that minimizes eq
.
In this question a previous discussion about a simular issue was made.
I tried this:
Minimize[eq, {xi, beta}]
and this:
dfunc = {D[eq, xi], D[eq, beta]};
Solve[dfunc == 0, {xi, beta}]
but I got no luck.
Any ideas? Is it possible to solve this analyticaly?
If we substitute numerical values to the constants and plot the funtion we get:
subst = {A -> 0.25, B -> 0.67, C -> 0.18, G -> 40, K -> 66.6667,
sig1tr -> -0, sig2tr -> -0.1, sig3tr -> -0.3};
pl = eq //. subst
Plot3D[pl, {xi, -0.5, 0.1}, {beta, 0, 2 Pi}]
Minimize[eq /. {A -> 0.25, B -> 0.67, C -> 0.18, G -> 40, K -> 66.6667, sig1tr -> -0, sig2tr -> -0.1, sig3tr -> -0.3}, {xi, beta}]
orMinimize[{eq, -Pi < beta <= Pi} /. {A -> 0.25, B -> 0.67, C -> 0.18, G -> 40, K -> 66.6667, sig1tr -> -0, sig2tr -> -0.1, sig3tr -> -0.3}, {xi, beta}]
$\endgroup$ – Bob Hanlon Dec 22 '18 at 19:12