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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>,
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* {{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=353–360|issn=0377-2217|doi=10.1016/0377-2217(91)90267-Y}}
* {{cite journal|ref=harv|title=Pseudo-Convex Functions|journal=Journal of the Society for Industrial and Applied Mathematics Series A|volume=3|issue=2|pages=281–290 |month=January|year=1965|doi=10.1137/0303020|first=O. L.|last=Mangasarian|issn=0363-0129}}
== Further reading ==
* {{cite journal|ref=harv|journal=Mathematical Programming|volume=28|issue=2|pages=226–239|doi=10.1007/BF02612363|title=Pseudolinearity and efficiency|first1=Kim Lin|last1=Chew|first2=Eng Ung|last2=Choo|year=1984}}
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* {{cite journal|ref=harv|first1=Giorgio|last1=Giorgi|first2=Norma G.|last2=Rueda|title=η-Pseudolinearity and Efficiency|journal=International Journal of Optimization: Theory, Methods and Applications|issn=2070-5565|year=2009|volume=1|issue=2|pages=155–159|format=[[Portable Document Format|PDF]]|url=http://www.gip.hk/ijotma/Internet%20IJOTMA%20V1N2/IJOTMAV1N2%20PA/IJOTMAv1n2%20pa3.pdf}}
* {{cite book|ref=harv|chapter=Generalized convexity and optimization: theory and applications|volume=616|series=Lecture Notes in Economics and Mathematical Systems|first1=Alberto|last1=Cambini|first2=Laura|last2=Martein|publisher=Springer|year=2009|isbn10=3540708758|isbn=9783540708759|chapter=Section 3.3: Quasilinearity and Pseudolinearity|pages=50–57|doi=10.1007/978-3-540-70876-6}}
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