Pseudolinear function: Difference between revisions

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

A function <math>f:X\rightarrow\mathbb{R}</math> is said to be '''pseudoconvex''' in <math>X\subseteq\mathbb{R}</math> if it is differentiable in <math>X</math> and for any <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 for <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}}