%\def\qed{$\Box$}
\def\bp{\asymp}
\def\uuu#1{{\accent"15 #1}}
\def\0{{\bf 0}}
\def\A{{\bf A}}
\def\a{{\bf a}}
\def\B{{\bf B}}
\def\b{{\bf b}}
\def\C{{\bf C}}
\def\c{{\bf c}}
\def\D{{\bf D}}
\def\E{{\bf E}}
\def\e{{\bf e}}
\def\F{{\bf F}}
\def\f{{\bf f}}
\def\G{{\bf G}}
\def\g{{\bf g}}
\def\H{{\bf H}}
\def\h{{\bf h}}
\def\I{{\bf I}}
\def\J{{\bf J}}
\def\i{\mbox{\boldmath$i$}}
\def\k{{\bf k}}
\def\K{{\bf K}}
\def\j{\mbox{\boldmath$j$}}
\def\L{{\bf L}}
\def\l{{\bf l}}
\def\M{{\bf M}}
%\newcommand{\M}{\mathbf{M}}
\def\m{{\bf m}}
\def\N{{\bf N}}
\def\n{{\bf n}}
\def\p{{\bf p}}
\def\P{{\bf P}}
\def\Q{{\bf Q}}
\def\q{{\bf q}}
\def\R{{\bf R}}
\def\r{{\bf r}}
\def\S{{\bf S}}
\def\s{{\bf s}}
\def\T{{\bf T}}
\def\t{{\bf t}}
\def\U{{\bf U}}
\def\V{{\bf V}}
\def\v{{\bf v}}
\def\W{{\bf W}}
\def\w{{\bf w}}
\def\u{{\bf u}}
\def\X{{\bf X}}
\def\x{{\bf x}}
\def\Y{{\bf Y}}
\def\y{{\bf y}}
\def\Z{{\bf Z}}
\def\z{{\bf z}}
\def\tr{{\rm tr}\;}
\def\pmb#1{\setbox0=\hbox{$#1$}%
        \kern-.025em\copy0\kern-\wd0
        \kern.05em\copy0\kern-\wd0
        \kern-.025em\raise.0433em\box0 }
%%\def\thefigure{\arabic{figure}}
\newtheorem{algorithm}{Algorithm}[section]
\newtheorem{assumption}{Assumption}[section]
\newtheorem{conjecture}{Conjecture}[section]
\newtheorem{corollary}{Corollary}[section]
\newtheorem{definition}{Definition}[section]
\newtheorem{example}{Example}[section]
\newtheorem{lemma}{Lemma}[section]
\newtheorem{observation}{Observation}[section]
\newtheorem{problem}{Problem}[section]
\newtheorem{project}{Project}[section]
\newtheorem{proposition}{Proposition}[section]
\newtheorem{remark}{Remark}[section]
\newtheorem{theorem}{Theorem}[section] %%%%%%
\newenvironment{Algorithm}{\begin{algorithm}\rm }{\end{algorithm}}
\newenvironment{Assumption}{\begin{assumption}\rm }{\end{assumption}}
\newenvironment{Definition}{\begin{definition}\rm }{\end{definition}}
\newenvironment{Example}{\begin{example}\rm }{\end{example}}
\newenvironment{Lemma}{\begin{lemma}\rm }{\end{lemma}}
\newenvironment{Observation}{\begin{observation}\rm }{\end{observation}}
\newenvironment{Problem}{\begin{problem}\rm }{\end{problem}}
%\newenvironment{Project}{\begin{project}\rm }{\end{project}}
\newenvironment{Proposition}{\begin{proposition}\rm }{\end{proposition}}
\newenvironment{Remark}{\begin{remark}\rm }{\end{remark}}
\newenvironment{Theorem}{\begin{theorem}\rm }{\end{theorem}} %%%%%%
\def\d{\displaystyle}
\def\sqr#1#2{{\vcenter{\hrule height.#2pt
      \hbox{\vrule width.#2pt height#1pt \kern#1pt
         \vrule width.#2pt}
      \hrule height.#2pt}}}
\def\square{\mathchoice\sqr34\sqr34\sqr{2.1}3\sqr{1.5}3}
\newtheorem{Thm}{Theorem}[section]
\newtheorem{Rem}[Thm]{Remark}
%teboulle
%\def\dom{\displaystyle\mathop {\mbox{dom}}}
\def\dom{\displaystyle\mathop {\mbox{\rm dom}}}
\def\breg{D_{\psi}}
\def\cis{d_{\varphi}}
\def\dpsi{\nabla \psi}
\def\tzer{\rightarrow 0}
\def\breg{D_{\psi}}
\def\cis{d_{\varphi}}
\newcommand{\beq}{\begin{equation}}
\newcommand{\eeq}{\end{equation}}
\newenvironment{proof}{\addvspace{\medskipamount}\par\noindent{\it Proof\/}:}%
{\unskip\nobreak\hfill\par\addvspace{\medskipamount}}

