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gitweb.michael.orlitzky.com - mjotex.git/blob - mjo-cone.tex
4 % The operator families Z(K), LL(K), etc. can technically be defined on
5 % sets other than cones, but nobody cares.
10 % The set of all S-operators on its argument.
11 \newcommand*
{\Sof}[1]{ \mathbf{S
} \of{ {#1} } }
13 % The cone of all Z-operators on its argument.
14 \newcommand*
{\Zof}[1]{ \mathbf{Z
} \of{ {#1} } }
16 % The space of Lyapunov-like operators on its argument.
17 \newcommand*
{\LL}[1]{ \mathbf{LL
}\of{ {#1} } }
19 % Display a ``Discrete Complementarity Set'' (DCS). The first argument
20 % is the name of the cone, the second argument is a generating set for
21 % that cone, and the third argument is a generating set for its dual.
22 \newcommand*
{\DCS}[3]{ C
\of{{#1}} \cap \qty{ {#2} \times {#3} } }
24 % Cone inequality operators.
25 \newcommand*
{\gek}{ \succcurlyeq }
26 \newcommand*
{\gtk}{ \succ }
27 \newcommand*
{\lek}{ \preccurlyeq }
28 \newcommand*
{\ltk}{ \prec }
30 % Starred versions of the cone inequality operators.
31 \newcommand*
{\ineqkstar}[1]{ \mathrel{ \overset{ _
{\ast} }{ #1 } } }
32 \newcommand*
{\gekstar}{ \ineqkstar{\gek} }
33 \newcommand*
{\gtkstar}{ \ineqkstar{\gtk} }
34 \newcommand*
{\lekstar}{ \ineqkstar{\lek} }
35 \newcommand*
{\ltkstar}{ \ineqkstar{\ltk} }
37 % And negated versions of some of those...
38 \newcommand*
{\ngeqkstar}{ \ineqkstar{\nsucceq} }
39 \newcommand*
{\ngtrkstar}{ \ineqkstar{\nsucc} }