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Minimize and solve large equation?

Posted 8 years ago

I have a complicated (looking) equation Gq, that I'm looking to minimize:

Gq = {b \[Gamma] - (E^((b Sqrt[\[Mu]^2 + 
             2 \[Lambda] \[Sigma]^2])/\[Sigma]^2) (E^((b Sqrt[\[Mu]^2 \
+ 2 \[Lambda] \[Sigma]^2])/\[Sigma]^2) mc + 
        E^((b \[Mu])/\[Sigma]^2) me) ((E^((b Sqrt[\[Mu]^2 + 
                  2 \[Lambda] \[Sigma]^2])/(2 \[Sigma]^2)) Sqrt[
            E^((b Sqrt[\[Mu]^2 + 
                    2 \[Lambda] \[Sigma]^2])/\[Sigma]^2) mc + 
             E^((b \[Mu])/\[Sigma]^2) me])/
         Sqrt[mc + 
           E^((b (\[Mu] + 
                   Sqrt[\[Mu]^2 + 
                    2 \[Lambda] \[Sigma]^2]))/\[Sigma]^2) me])^(-1 - \
\[Mu]/Sqrt[\[Mu]^2 + 2 \[Lambda] \[Sigma]^2]) (-\[Mu]^2 - 
        2 \[Lambda] \[Sigma]^2 + \[Mu] Sqrt[\[Mu]^2 + 
           2 \[Lambda] \[Sigma]^2]))/((-1 + 
        E^((2 b Sqrt[\[Mu]^2 + 
               2 \[Lambda] \[Sigma]^2])/\[Sigma]^2)) \[Lambda] \
(-\[Mu] + Sqrt[\[Mu]^2 + 2 \[Lambda] \[Sigma]^2]))} 

I tried Minimize[Gq,b] directly but it just hangs. Then I tried solve D by taking the derivative and setting to zero (it's a convex function), including all of the positivity and non-negativity conditions that should make it easier to solve.

Solve[D[Gq, b] == 0 && b > 0 && \[Lambda] > 0 && \[Sigma] > 0 && me > 0 && mc > 0, b]

But it still continues to hang and doesn't compute. Your help would be VERY much appreciated. Even when I continue to substitute more direct values

me == 0.005 && mc = 0.0075 && \[Lambda] == 0.1 && \[Sigma] > 10000 && \[Mu] == -10000

so that the only free variable is b, it still doesn't solve it.

2 Replies

Thanks for point it out -- it should be corrected. Thanks in advance for your help!

Your expression does not parse correctly

Gq = {b[Gamma] - (E^((b Sqrt[[Mu]^2 + 
             2[Lambda][
               Sigma]^2])/[Sigma]^2) (E^((b Sqrt[[Mu]^2 + 
                2[Lambda][Sigma]^2])/[Sigma]^2) mc + 
        E^((b[Mu])/[Sigma]^2) me) ((E^((b Sqrt[[Mu]^2 + 
                  2[Lambda][Sigma]^2])/(2[Sigma]^2)) Sqrt[
            E^((b Sqrt[[Mu]^2 + 2[Lambda][Sigma]^2])/[Sigma]^2) mc + 
             E^((b[Mu])/[Sigma]^2) me])/
         Sqrt[mc + 
           E^((b ([Mu] + 
                   Sqrt[[Mu]^2 + 
                    2[Lambda][Sigma]^2]))/[Sigma]^2) me])^(-1 - [Mu]/
          Sqrt[[Mu]^2 + 2[Lambda][Sigma]^2]) (-[Mu]^2 - 
        2[Lambda][
          Sigma]^2 + [Mu] Sqrt[[Mu]^2 + 2[Lambda][Sigma]^2]))/((-1 + 
         E^((2 b Sqrt[[Mu]^2 + 2[Lambda][Sigma]^2])/[Sigma]^2))[
       Lambda] (-[Mu] + Sqrt[[Mu]^2 + 2[Lambda][Sigma]^2]))}

Syntax::sntxb: Expression cannot begin with "[Mu]^2".
POSTED BY: Frank Kampas
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