--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/doc/symbols.tex Fri Mar 28 08:36:08 2025 -0500 @@ -0,0 +1,166 @@ +\newcommand{\term}{\emph} + +\newcommand{\field}[1]{\mathbb{#1}} +\newcommand{\N}{\mathbb{N}} +\newcommand{\Z}{\mathbb{Z}} +\newcommand{\Q}{\field{Q}} +\newcommand{\R}{\field{R}} +\newcommand{\extR}{\overline \R} +\newcommand{\Complex}{\field{C}} +\newcommand{\B}{\mathbb{B}} +\newcommand{\OB}{\mathbb{O}} +%\newcommand{\UU}{\mathbb{U}} +% Trust regions are just normal balls. +\let\UU\B +\newcommand{\norm}[1]{\|#1\|} +\newcommand{\adaptnorm}[1]{\left\|#1\right\|} +\newcommand{\bignorm}[1]{\bigl\|#1\bigr\|} +\newcommand{\Bignorm}[1]{\Bigl\|#1\Bigr\|} +\newcommand{\abs}[1]{|#1|} +\newcommand{\adaptabs}[1]{\left|#1\right|} +\newcommand{\bigabs}[1]{\bigl|#1\bigr|} +\newcommand{\inv}[1]{#1^{-1}} +\newcommand{\grad}{\nabla} +\newcommand{\freevar}{\,\boldsymbol\cdot\,} +\newcommand{\Union}\bigcup +\newcommand{\Isect}\bigcap +\newcommand{\union}\cup +\newcommand{\isect}\cap +\newcommand{\bigunion}\bigcup +\newcommand{\bigisect}\bigcap +\newcommand{\powerset}{\mathcal{P}} +\newcommand{\defeq}{:=} +\newcommand{\set}[1]{\{#1\}} +\newcommand{\downto}{\searrow} +\newcommand{\upto}{\nearrow} +\newcommand{\subdiff}{\partial} +\newcommand{\pinv}[1]{#1^\dag} +\newcommand{\overbar}[1]{\mkern 1.5mu\overline{\mkern-1.5mu#1\mkern-1.5mu}\mkern 1.5mu} + +\DeclareMathOperator*{\lip}{lip} +\DeclareMathOperator*{\argmin}{arg\,min} +\DeclareMathOperator*{\argmax}{arg\,max} +\DeclareMathOperator{\interior}{int} +\DeclareMathOperator{\ri}{ri} +\DeclareMathOperator{\rbd}{rbd} +\DeclareMathOperator{\closure}{cl} +\DeclareMathOperator{\bd}{bd} +\DeclareMathOperator{\sign}{sign} +\DeclareMathOperator{\Sign}{Sign} +\DeclareMathOperator{\rank}{rank} +\DeclareMathOperator{\range}{ran} +\DeclareMathOperator{\dom}{dom} +\DeclareMathOperator{\cod}{cod} +\DeclareMathOperator{\lev}{lev} +\DeclareMathOperator{\conv}{conv} +\DeclareMathOperator{\diam}{diam} +\DeclareMathOperator{\epi}{epi} +\DeclareMathOperator{\tr}{tr} +\DeclareMathOperator{\diag}{diag} +\DeclareMathOperator{\graph}{graph} +\DeclareMathOperator{\cond}{cond} +\DeclareMathOperator{\esssup}{ess\,sup} +\DeclareMathOperator{\support}{supp} +\DeclareMathOperator{\divergence}{div} +\DeclareMathOperator{\Id}{Id} +\DeclareMathOperator{\dist}{dist} +\DeclareMathOperator{\Sym}{Sym} +\DeclareMathOperator{\prox}{prox} +\DeclareMathOperator{\gdesc}{g-desc} +\DeclareMathOperator{\gexp}{g-exp} +\DeclareMathOperator{\desc}{desc} + +\newcommand{\mathvar}[1]{\textup{#1}} + +\newcommand{\iprod}[2]{\langle #1,#2\rangle} +%\newcommand{\dualprod}[2]{\langle #1 | #2\rangle} +\newcommand{\dualprod}[2]{\langle #1,#2\rangle} +\newcommand{\adaptiprod}[2]{\left\langle #1,#2\right\rangle} + +\newcommand{\weakto}{\mathrel{\rightharpoonup}} +%\makeatletter +\def \weaktostarSym{\setbox0=\hbox{$\rightharpoonup$}\rlap{\hbox + to\wd0{\hss\raise1ex\hbox{$\scriptscriptstyle{*\,}$}\hss}}\box0} + \def \weaktostar {\mathrel{\weaktostarSym}} +%\makeatother + +\newcommand{\setto}{\rightrightarrows} + +\def\opt#1{\bar #1} +\def\realopt#1{\widehat #1} +\def\dir#1{\Delta #1} +\def\alt#1{\tilde #1} +\def\altalt#1{#1'} +\def\this#1{#1^k} +\def\nexxt#1{#1^{k+1}} +\def\overnext#1{\bar #1^{k+1}} +\def\prev#1{#1^{k-1}} +\def\thisstar#1{#1^k^*} +\def\nextstar#1{#1^{k+1}^*} +\def\optstar#1{\opt{#1}^*} +\def\realoptstar#1{\realopt{#1}^*} + +\def\optu{{\opt{u}}} +\def\optv{{\opt{v}}} +\def\optw{{\opt{w}}} +\def\optx{{\opt{x}}} +\def\opty{{\opt{y}}} +\def\optz{{\opt{z}}} + +\def\realoptu{{\realopt{u}}} +\def\realoptv{{\realopt{v}}} +\def\realoptw{{\realopt{w}}} +\def\realoptx{{\realopt{x}}} +\def\realopty{{\realopt{y}}} +\def\realoptz{{\realopt{z}}} + +\def\nextu{\nexxt{u}} +\def\nextv{\nexxt{v}} +\def\nextw{\nexxt{w}} +\def\nextx{\nexxt{x}} +\def\nexty{\nexxt{y}} +\def\nextz{\nexxt{z}} + +\def\thisu{\this{u}} +\def\thisv{\this{v}} +\def\thisw{\this{w}} +\def\thisx{\this{x}} +\def\thisy{\this{y}} +\def\thisz{\this{z}} + +\def\prevu{\prev{u}} +\def\prevv{\prev{v}} +\def\prevw{\prev{w}} +\def\prevx{\prev{x}} +\def\prevy{\prev{y}} +\def\prevz{\prev{z}} + +\def\overnextu{\overnext{u}} +\def\overnextx{\overnext{x}} + +\def\d{\,\mathrm{d}} + +\let\altphi\phi +\let\phi\varphi +\let\altepsilon\epsilon +\let\epsilon\varepsilon + +\newcommand{\frechetNormal}{\widehat N} +\newcommand{\frechetCod}{\widehat D^*} +\newcommand{\clarkeTangent}{\widehat T} +\newcommand{\clarkeGD}{\widehat D} +\newcommand{\coderivative}{D^*} +\newcommand{\polar}[1]{#1^{\circ}} +\newcommand{\bipolar}[1]{#1^{\circ\circ}} +\newcommand{\upperadj}[1]{#1^{\circ+}} +\newcommand{\loweradj}[1]{#1^{\circ-}} + +\def\invstar#1{{#1}^{-1,*}} +\def\pinvstar#1{{#1}^{\dagger*}} +\def\starpinv#1{{#1}^{*\dagger}} + +\def\linear{\mathbb{L}} + +\def\QL{\mathop{QL}\nolimits} + +\def\lebesgue{\mathcal{L}}