Pseudolinear function: Difference between revisions

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AIn mathematics, a '''pseudoconvex function''' <math>f:X\rightarrow\mathbb{R}</math> ison saida to be '''pseudoconvex''' inset <math>X\subseteq\mathbb{R}</math> ifis a function itthat is differentiable in <math>X</math> andsuch that for anyevery <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>.

It is '''pseudoconcave''' if this is true forof <math>-f</math>.

A '''pseudolinear function''' is one that is both pseudoconvex and pseudoconcave.

== References ==

* {{cite journal|ref=harv|first=T.|last=Rapcsak|title=On pseudolinear functions|journal=European Journal of Operational Research|volume=50|issue=3|day=15|month=February|year=1991|pages=353&ndash;360|issn=0377-2217|doi=10.1016/0377-2217(91)90267-Y}}