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It is easy to verify that x is a solution of (1) if and only if it is an optimal solution of the following problems with zero objective value: begin{aligned} min&quad Psi(x) mathrm{s.t.}&quad xinRe_^{n}, end{aligned} (2) where (Re_^{n}: = {xinRe^{n} | xgeq0 }), (Psi(x)=frac{1}{2} Vert Phi(x) Vert ^{2}), and (Phi(x): = (phi(F_{1}(x),x_{1}), ldots, phi(F_{n}(x),x_{n}))^{T} ).
It should furthermore be noted that asserting the existence of something for which there is zero objective evidence is widely viewed as a form of pseudo-science.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com