
\documentclass[11pt]{article}

\usepackage{alltt}
\usepackage{graphicx}
\usepackage[dvips]{epsfig}
% New mathematical facilities like \mathbb, \big, and \mapsto
\usepackage{amssymb}
% Defines page size and margins.
\input{../sty/preamble}
% Redefines the size of the section headings.
\usepackage{../sty/art11mod}
% The float package is described in page 146 of the LaTeX companion.
\usepackage{../sty/float}
% Numbers equations,... consecutively within sections.
\usepackage{../sty/numinsec}
% The bar package is described in page 283 of the LaTeX companion.
\usepackage{../sty/bar}
% The url package is intended for email addresses, hypertext links, ...
\usepackage{../sty/url}

\newcommand{\R}{\mbox{${\mathbb R}$}}

\begin{document}

\setlength{\baselineskip}{15pt}

\pagestyle {plain}

\subsection*{Notes for Referee 1}


\begin{center}
\textbf{A Case Study in the Performance and Scalability of
Optimization Algorithms}
\end{center}

Thank you for your comments on the paper. They are very much
appreciated.
We have changed the report according to your comments and those
of the other referee. Note, in particular, that the title is now changed.
Below are notes on our changes. 

\begin{enumerate}
\item
The notation $ f : \R^n \mapsto \R^m $ seems to be quite natural.
You can read this as saying that $f$ maps $ \R^n $ to $ \R^m $.
You can also read 
$ \alpha \mapsto 
q \left (y_k - \alpha  \nabla_{\Omega} q(y_k) \right ) $ 
in the same way.
We realize that other authors use the somewhat more standard
notation $ \to $ in the first case, but the meaning is clear in both cases.
\item
Changed.
\item
Agreed. They have been changed.
\item
Replace $y$ by $v$. This should eliminate any confusion.
\item
We now say that $ \eta_1 $ is a constant in $ (0,1) $.
\item
Good point. We re-organized these sentences.
\item
Checked. The title is correct.
\end{enumerate}




\end{document}



