mjo-convex.tex

   1 %
   2 % Operations that usually appear in convex optimization.
   3 %
   4 \ifx\havemjoconvex\undefined
   5 \def\havemjoconvex{1}
   6
   7
   8 % Needed for \operatorname.
   9 \usepackage{amsopn}
  10
  11 \input{mjo-common}
  12
  13 % The ``conic combination'' operator.
  14 \newcommand*{\cone}[1]{ \operatorname{cone} \of{{#1}} }
  15
  16 % The ``convex hull'' operator.
  17 \newcommand*{\conv}[1]{ \operatorname{conv} \of{{#1}} }
  18
  19 % The ``affine hull'' operator.
  20 \newcommand*{\aff}[1]{ \operatorname{aff} \of{{#1}} }
  21
  22 % The ``lineality space'' operator.
  23 \newcommand*{\linspace}[1]{ \operatorname{linspace} \of{{#1}} }
  24
  25 % The ``lineality'' operator.
  26 \newcommand*{\lin}[1]{ \operatorname{lin} \of{{#1}} }
  27
  28 % The ``Extreme vectors'' (or ``Extreme directions'') operator.
  29 \newcommand*{\Ext}[1]{ \operatorname{Ext} \of{{#1}} }
  30
  31 % The "is a face of" and "is a proper face of" relations.
  32 \newcommand*{\faceof}{ \trianglelefteq }
  33 \newcommand*{\properfaceof}{ \triangleleft }
  34
  35
  36 \fi