# Plotting NMinimize function

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[BoxForme, MatrixForm[BoxForme]]]$$;
{\[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

• Please provide your complete code , not an image. Thanks! Commented Jan 23, 2020 at 17:15
• I have added the code. Please take a look. Thanks Commented Jan 23, 2020 at 19:36

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]