mjo-convex.tex

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