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Let x̅ ∈ E be a weak efficient solution of (P).
Let be a weak efficient solution of (WHP).
Let be a weak efficient solution of (WHD).
Let f : S 1 × S 2 → R k be a twice differentiable function and let ( x ¯, y ¯, λ ¯, z ¯, p ¯ ) be a weak efficient solution of (HNWP).
A point x ̄ ∈ X is said to be a weak efficient solution for (MP), if there exists no x ∈ X such that F ( x ) < F ( x ̄ ).
Let f : S 1 × S 2 → R k be a twice differentiable function and let ( u ¯, v ¯, λ ¯, w ¯, r ¯ ) be a weak efficient solution of (HNWD).
Similar(51)
Therefore, x ̄ is a weak efficient solution for (VFP).
Then x ̄ is a weak efficient solution for (VFP).
Hence, x* is a weak efficient solution of (P).
A point is a weak efficient solution of (P) if there exists no such that.
If (bar{x}in X) is a weak efficient solution of (MP), then x̄ solves (MVVI).
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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