Editing Convex set (section)

=== Non-convex set ===
A set that is not convex is called a ''non-convex set''. A [[polygon]] that is not a [[convex polygon]] is sometimes called a [[concave polygon]],<ref>{{cite book |first=Jeffrey J. |last=McConnell |year=2006 |title=Computer Graphics: Theory Into Practice |isbn=0-7637-2250-2 |page=[https://archive.org/details/computergraphics0000mcco/page/130 130] |publisher=Jones & Bartlett Learning |url=https://archive.org/details/computergraphics0000mcco/page/130 }}.</ref> and some sources more generally use the term ''concave set'' to mean a non-convex set,<ref>{{MathWorld|title=Concave|id=Concave}}</ref> but most authorities prohibit this usage.<ref>{{cite book|title=Analytical Methods in Economics|first=Akira|last=Takayama|publisher=University of Michigan Press|year=1994|isbn=9780472081356|url=https://books.google.com/books?id=_WmZA0MPlmEC&pg=PA54|page=54|quote=An often seen confusion is a "concave set". Concave and convex functions designate certain classes of functions, not of sets, whereas a convex set designates a certain class of sets, and not a class of functions. A "concave set" confuses sets with functions.}}</ref><ref>{{cite book|title=An Introduction to Mathematical Analysis for Economic Theory and Econometrics|first1=Dean|last1=Corbae|first2=Maxwell B.|last2=Stinchcombe|first3= Juraj|last3=Zeman|publisher=Princeton University Press|year=2009|isbn=9781400833085|url=https://books.google.com/books?id=j5P83LtzVO8C&pg=PT347|page=347|quote=There is no such thing as a concave set.}}</ref>

The [[Complement (set theory)|complement]] of a convex set, such as the [[epigraph (mathematics)|epigraph]] of a [[concave function]], is sometimes called a ''reverse convex set'', especially in the context of [[mathematical optimization]].<ref>{{cite journal | last = Meyer | first = Robert | journal = SIAM Journal on Control and Optimization | mr = 0312915 | pages = 41–54 | title = The validity of a family of optimization methods | volume = 8 | year = 1970| doi = 10.1137/0308003 | url = https://minds.wisconsin.edu/bitstream/handle/1793/57508/TR28.pdf?sequence=1 }}.</ref>