Add some common cones to mjo-cone.

[mjotex.git] / mjo-cone.tex

diff --git a/mjo-cone.tex b/mjo-cone.tex
index e35b5eb4babb13b16b202f1c52acd50a1076b3d2..1199d4f55be54130d2660f7814f9f857d8590853 100644 (file)
--- a/mjo-cone.tex
+++ b/mjo-cone.tex
@@ -5,8 +5,31 @@
 % sets other than cones, but nobody cares.
 %
 
+\usepackage{amssymb} % \succcurlyeq and friends
+
 \input{mjo-common}
 
+%
+% Common cones.
+%
+
+% The nonnegative orthant in the given number of dimensions.
+\newcommand*{\Rnplus}[1][n]{ \mathbb{R}^{{#1}}_{+} }
+
+% The Lorentz ``ice-cream'' cone in the given number of dimensions.
+\newcommand*{\Lnplus}[1][n]{ \mathcal{L}^{{#1}}_{+} }
+
+% The PSD cone in a space of symmetric matrices.
+\newcommand*{\Snplus}[1][n]{ \mathcal{S}^{{#1}}_{+} }
+
+% The PSD cone in a space of Hermitian matrices.
+\newcommand*{\Hnplus}[1][n]{ \mathcal{H}^{{#1}}_{+} }
+
+
+%
+% Some collections of linear operators
+%
+
 % The set of all S-operators on its argument.
 \newcommand*{\Sof}[1]{ \mathbf{S} \of{ {#1} } }
 
@@ -16,17 +39,18 @@
 % The space of Lyapunov-like operators on its argument.
 \newcommand*{\LL}[1]{ \mathbf{LL}\of{ {#1} } }
 
-% Display a ``Discrete Complementarity Set'' (DCS). The first argument
-% is the name of the cone, the second argument is a generating set for
-% that cone, and the third argument is a generating set for its dual.
-\newcommand*{\DCS}[3]{ C\of{{#1}} \cap \qty{ {#2} \times {#3} } }
 
+%
 % Cone inequality operators.
+%
+
+% Standard cone inequalities.
 \newcommand*{\gek}{ \succcurlyeq }
 \newcommand*{\gtk}{ \succ }
 \newcommand*{\lek}{ \preccurlyeq }
 \newcommand*{\ltk}{ \prec }
 
+
 % Starred versions of the cone inequality operators.
 \newcommand*{\ineqkstar}[1]{ \mathrel{ \overset{ _{\ast} }{ #1 } } }
 \newcommand*{\gekstar}{ \ineqkstar{\gek} }