% Operations that usually appear in convex optimization.
%
+% Needed for \operatorname.
+\usepackage{amsopn}
+
\input{mjo-common}
% The ``conic combination'' operator.
% 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 }