Plotting NMinimize function

Question

I want to plot the following NMinimize function:

I used

GGPlot = Plot[GG[DM], {DM, 0.02, 10}, PlotRange -> All]

But I get nothing! My code is

GG[DM_] := (
  \[CapitalLambda]u = \!\(\*
TagBox[
RowBox[{"(", "", GridBox[{
{"\[Theta]", "\[Phi]", "0", 
RowBox[{"2", "\[Theta]"}]},
{"0", "6", 
RowBox[{"8", "DM"}], "\[Phi]"},
{"0", 
RowBox[{"42", "+", "DM"}], "\[Theta]", "0"},
{"5", "0", "\[Phi]", "20"}
},
GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.7]}, 
Offset[0.27999999999999997`]}, "Rows" -> {
Offset[0.2], {
Offset[0.4]}, 
Offset[0.2]}}], "", ")"}],
Function[BoxForm`e$, 
MatrixForm[BoxForm`e$]]]\);
  {\[Omega]1, \[Omega]2, \[Omega]3, \[Omega]4} = 
   Chop[Eigenvalues[\[CapitalLambda]u]];

  FMin = 1/
    2 Chop[NMinimize[{Tr[\[CapitalLambda]u] + (Abs[\[Omega]1] + 
          Abs[\[Omega]1] + Abs[\[Omega]1] + 
          Abs[\[Omega]1]), {\[Theta]} \[Element] 
        Interval[{0, (3 \[Pi])/2}], {\[Phi]} \[Element] 
        Interval[{0, (3 \[Pi])/2}]}, {\[Theta], \[Phi]}]];  
  (1 - Sqrt[FMin]) )

I want to plot this NMinimize function,I want to plot the following NMinimize function:I want to plot the following NMinimize

Answer 1

I made a little change to the four times Abs[w1]. Think it was a typo.

\[CapitalLambda]u = {{\[Theta], \[Phi], 0, 2*\[Theta]}, 
   {0, 6, 8*DM, \[Phi]}, {0, DM + 42, \[Theta], 0}, 
   {5, 0, \[Phi], 20}}

{\[Omega]1, \[Omega]2, \[Omega]3, \[Omega]4} = 
Eigenvalues[\[CapitalLambda]u]

ff[DM_, \[Theta]_, \[Phi]_] = {Tr[\[CapitalLambda]u] + 
Sqrt[\[Omega]1^2] + 
          Sqrt[\[Omega]2^2] + Sqrt[\[Omega]3^2] + 
          Sqrt[\[Omega]4^2], 
    0 < \[Theta] < (3 \[Pi])/2 && 0 < \[Phi] < (3 \[Pi])/2} // Simplify

nmin[DM_?NumericQ] := 
  NMinimize[ff[DM, \[Theta], \[Phi]], {\[Theta], \[Phi]}]

GG[DM_] := 1 - Sqrt[1/2*First@nmin[DM]]

GGPlot = Plot[GG[DM], {DM, 0.02, 10}, PlotRange -> All, 
            PlotPoints -> 15, MaxRecursion -> 1]