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Again, let (mathbf {Q}=mathbf {R}_{x_{0}} geq 0) and (mathbf {P}=mathsf {E}_{mathbf {G}_{N}}left {mathbf {G}_{N}^{H}mathbf {R}_{dot {n}}^{-1}mathbf {G}_{N}right }>0), it can be seen that Problem (15) is now in the form of (11), and hereby, the solution to (15) can be optimally obtained.
It can easily be seen that problem (1), (2), and (23) are equivalent in the following sense: if x = ( u, α ) is a solution to (23), then α i = 0 ( i = 1, …, n ) and ( u i ) i = 1 n is a solution to (1), (2); and vice versa if ( u i ) i = 1 n is a solution to (1), (2), then x = ( u, 0 ) is a solution to (23).
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com