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In mathematics, a '''pseudoconvex function''' <math>f:X\rightarrow\mathbb{R}</math> on an open convex set <math>X\subseteq\mathbb{R}^n</math> is a function that is differentiable in <math>X</math> such that for every <math>x,y\in X</math>,
:<math>f\left(y\right)<f\left(x\right)\Rightarrow\left(y-x\right)^{T}\nabla f\left(x\right)<0. \, </math>
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