X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo-convex.tex;h=a51011f4613ef1e0635d4f73e2b567b2afd3e598;hb=a9aeb1d067a05434e80f85edb74685737e6c99ea;hp=f482f9f2fa4eeac75155f05893fc3a3fe4f5bfc8;hpb=d6a9f13f45fead88404ee02cb446db2f3047eee8;p=mjotex.git

diff --git a/mjo-convex.tex b/mjo-convex.tex
index f482f9f..a51011f 100644
--- a/mjo-convex.tex
+++ b/mjo-convex.tex
@@ -2,6 +2,9 @@
 % Operations that usually appear in convex optimization.
 %
 
+% Needed for \operatorname.
+\usepackage{amsopn}
+
 \input{mjo-common}
 
 % The ``conic combination'' operator.
@@ -19,5 +22,9 @@
 % The ``lineality'' operator.
 \newcommand*{\lin}[1]{ \operatorname{lin} \of{{#1}} }
 
-% The ``Exteme vectors'' operator.
+% The ``Extreme vectors'' (or ``Extreme directions'') operator.
 \newcommand*{\Ext}[1]{ \operatorname{Ext} \of{{#1}} }
+
+% The "is a face of" and "is a proper face of" relations.
+\newcommand*{\faceof}{ \trianglelefteq }
+\newcommand*{\properfaceof}{ \triangleleft }