fixed the references

OpSplit.bib

@@ -166,10 +166,16 @@ @inproceedings{combettes2014forward
 @article{davis2014convergence,
   title={Convergence rate analysis of primal-dual splitting schemes},
   author={Davis, Damek},
-  journal={arXiv preprint arXiv:1408.4419},
-  year={2014}
+  journal={SIAM Journal on Optimization},
+  volume={25},
+  number={3},
+  pages={1912--1943},
+  year={2015},
+  publisher={SIAM}
 }
 
+
+
 @article{chambolle2011first,
   title={A first-order primal-dual algorithm for convex problems with applications to imaging},
   author={Chambolle, Antonin and Pock, Thomas},
@@ -247,7 +253,7 @@ @article{Strikwerda2002125
 
 @article{Patrick_2015,
 author = {Patrick L. Combettes and Jean-Christophe Pesquet},
-title = {Stochastic Quasi-Fejér Block-Coordinate Fixed Point Iterations with Random Sweeping},
+title = {Stochastic Quasi-Fej{\'e}r Block-Coordinate Fixed Point Iterations with Random Sweeping},
 journal = {SIAM Journal on Optimization},
 volume = {25},
 number = {2},
@@ -258,7 +264,7 @@ @article{Patrick_2015
 
 @ARTICLE{Peng_2015_AROCK,
    author = {{Peng}, Z. and {Xu}, Y. and {Yan}, M. and {Yin}, W.},
-    title = "{ARock: an Algorithmic Framework for Asynchronous Parallel Coordinate Updates}",
+    title = "{ARock: an algorithmic framework for asynchronous parallel coordinate updates}",
   journal = {ArXiv e-prints},
 archivePrefix = "arXiv",
    eprint = {1506.02396},

appendix.tex

@@ -41,15 +41,15 @@ \section{Some Key Concepts of Operator}\label{sec:op-concept}
  A special proximal map is the projection map. Let $X$ be a nonempty closed convex set, and $\iota_S$ be its indicator function. Minimizing $\iota_S(x)$  enforces $x\in S$,  so $\prox_{\gamma \iota_S}$ reduces to the projection map $\prj_{S}$ for any $\gamma>0$. Therefore, $\prj_{S}$ is also firmly nonexpansive.
  \end{example}
 
-\cut{A firmly nonexpansive operator is always nonexpansive and maximally monotone \cite[Example 20.27]{B-C2011cvx-mon}. }
+\cut{A firmly nonexpansive operator is always nonexpansive and maximally monotone \cite[Example 20.27]{bauschke2011convex}. }
 
 \begin{definition}[$\beta$-cocoercive operator]
 An operator $\cT:\HH\to\HH$ is \emph{$\beta$-cocoercive} if 
 $\langle x-y, \cT x-\cT y\rangle \ge \beta \|\cT x-\cT y\|^2,\ \forall x,y\in\HH.$ 
 \end{definition}
 
 \begin{example}
-A special example of  cocoercive operator is the gradient of a smooth function. Let $f$ be a differentiable function. Then $\nabla f$ is $\beta$-Lipschitz continuous \emph{if and only if} $\nabla f$ is $\frac{1}{\beta}$-cocoercive \cite[Corollary 18.16]{B-C2011cvx-mon}. \cut{If $\cT$ is $\beta$-cocoercive, $\beta \cT$ must be firmly nonexpansive \cite[Remark 4.24]{B-C2011cvx-mon}, and $\cT$ is maximally monotone.}
+A special example of  cocoercive operator is the gradient of a smooth function. Let $f$ be a differentiable function. Then $\nabla f$ is $\beta$-Lipschitz continuous \emph{if and only if} $\nabla f$ is $\frac{1}{\beta}$-cocoercive \cite[Corollary 18.16]{bauschke2011convex}. \cut{If $\cT$ is $\beta$-cocoercive, $\beta \cT$ must be firmly nonexpansive \cite[Remark 4.24]{bauschke2011convex}, and $\cT$ is maximally monotone.}
 \end{example}
 \cut{
 At last we give a counterexample to show naively extending existing algorithms to coordinate update schemes may result in divergence or wrong solutions.

asyn.bib

@@ -247,7 +247,7 @@ @article{bethune2014performance
 }
 
 @article{combettes2014stochastic,
-  title={Stochastic Quasi-Fej{\'e}r Block-Coordinate Fixed Point Iterations with Random Sweeping},
+  title={Stochastic Quasi-Fejer Block-Coordinate Fixed Point Iterations with Random Sweeping},
   author={Combettes, Patrick L and Pesquet, Jean-Christophe},
   journal={arXiv preprint arXiv:1404.7536},
   year={2014}

cu_opsplit.tex

@@ -10,7 +10,7 @@ \subsection{Operator Splitting Schemes}\label{sec:splitting}
 When $\cA, \cB$ are maximally monotone (think it as the subdifferential $\partial f$ of a proper convex function $f$) and $\cC$ is $\beta$-cocoercive (think it as the gradient $\nabla f$ of a $1/\beta$-Lipschitz differentiable function $f$),  a solution can be found by the iteration \eqref{fpi} with $\cT=\TS$, introduced recently in \cite{davis2015three}, where  \cut{three operator splitting (3S) for solving \eqref{eqn:3s_problem} is defined by}
 \beq\label{3s}
 \TS := \cI- \cJ_{\gamma \cB}+ \cJ_{\gamma \cA}\circ(2 \cJ_{\gamma \cB}- \cI - \gamma \cC\circ \cJ_{\gamma \cB}).
-\eeq \cut{It can be shown that if $\cC$ is $\beta$-cocoercive, then}Indeed, by setting  $\gamma\in(0,2\beta)$, $\cT_{3S}$ is $(\frac{2\beta}{4\beta-\gamma})$-averaged (think it as a property weaker than the Picard contraction that no longer garantees $\cT$ having a fixed point, yet ensures convergence where a fixed point does exist.). Following the standard convergence result (cf. textbook \cite{B-C2011cvx-mon}), provided that $\cT$ has a  fixed point, the sequence from~\eqref{fpi} converges to a fixed-point $x^*$ of $\TS$. Instead of $x^*$, $\cJ_{\gamma\cB}(x^*)$ is a solution to~\eqref{eqn:3s_problem}.  \cut{, and one can choose $\gamma\in(0,2\beta)$ for convergence.}
+\eeq \cut{It can be shown that if $\cC$ is $\beta$-cocoercive, then}Indeed, by setting  $\gamma\in(0,2\beta)$, $\cT_{3S}$ is $(\frac{2\beta}{4\beta-\gamma})$-averaged (think it as a property weaker than the Picard contraction that no longer garantees $\cT$ having a fixed point, yet ensures convergence where a fixed point does exist.). Following the standard convergence result (cf. textbook \cite{bauschke2011convex}), provided that $\cT$ has a  fixed point, the sequence from~\eqref{fpi} converges to a fixed-point $x^*$ of $\TS$. Instead of $x^*$, $\cJ_{\gamma\cB}(x^*)$ is a solution to~\eqref{eqn:3s_problem}.  \cut{, and one can choose $\gamma\in(0,2\beta)$ for convergence.}
 Applying the results in \S\ref{sc:comb},  $\TS$ {is CF if } $\cJ_{\gamma \cA}$ is separable ($\cC_1$). $\cJ_{\gamma \cB}$ is \cut{easy-to-compute or }Type-II CF ($\cF_2$), and $\cC$ is Type-I CF ($\cF_1$). %Given $x$, $(\cT_{3S} x)_i = ......$
 
 %\subsubsection{Special cases}