mjo-hurwitz.tex: new file for Hurwitz algebras (quaternions and octonions).
[mjotex.git] / 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