%\chapterauthor{Bastien Chopard}{Department of Computer Science, University of Geneva}
%\chapter{Linear programming on a GPU: a study case based on the simplex method and the branch-cut-and bound algorithm}
-\chapter{Linear Programming on a GPU: A~Case~Study}
+\chapter{Linear programming on a GPU: a~case~study}
\section{Introduction}
\label{chXXX:sec:intro}
The simplex method~\cite{VCLP} is a well-known optimization algorithm for solving linear programming (LP) models in the field of operations research. It is part of software often employed by businesses for finding solutions to problems such as airline scheduling problems. The original standard simplex method was proposed by Dantzig in 1947. A more efficient method, named the revised simplex, was later developed. Nowadays its sequential implementation can be found in almost all commercial LP solvers. But the always increasing complexity and size of LP problems from the industry, drives the demand for more computational power.
\begin{figure}[!h]
\centering
\includegraphics[width=10cm]{Chapters/chapter10/figures/Reduc3.pdf}
-\caption{Example of a parallel reduction at block level (courtesy NVIDIA).}
+\caption{Example of a parallel reduction at block level. (Courtesy NVIDIA).}
\label{chXXX:fig:reduc}
\end{figure}
