[tex] proof-read

tex/biblio.bib

@@ -196,7 +196,7 @@ @article{gould2001solution
   publisher={SIAM}
 }
 
-@software{jax2018github,
+@misc{jax2018github,
   author = {James Bradbury and Roy Frostig and Peter Hawkins and Matthew James Johnson and Chris Leary and Dougal Maclaurin and George Necula and Adam Paszke and Jake Vander{P}las and Skye Wanderman-{M}ilne and Qiao Zhang},
   title = {{JAX}: composable transformations of {P}ython+{N}um{P}y programs},
   url = {http://github.com/google/jax},
@@ -311,7 +311,7 @@ @article{shin2021graph
 }
 
 @article{montoison2023krylov,
-  title={Krylov. jl: A Julia basket of hand-picked Krylov methods},
+  title={Krylov. jl: A Julia basket of hand-picked {K}rylov methods},
   author={Montoison, Alexis and Orban, Dominique},
   journal={Journal of Open Source Software},
   volume={8},
@@ -378,7 +378,7 @@ @inproceedings{bischof1991exploiting
   year={1991}
 }
 
-@software{Montoison_CUDSS,
+@misc{Montoison_CUDSS,
   author = {Montoison, Alexis},
   license = {MIT},
   title = {{CUDSS.jl: Julia interface for NVIDIA cuDSS}},
@@ -397,17 +397,6 @@ @article{hestenes-stiefel-1952
  doi = {10.6028/jres.049.044}
 }
 
-@article{cao-seth-laird-2016,
-  title = {An augmented Lagrangian interior-point approach for large-scale NLP problems on graphics processing units},
-  author = {Cao, Yankai and Seth, Arpan and Laird, Carl D},
-  journal = {Computers \& Chemical Engineering},
-  volume = {85},
-  pages = {76--83},
-  year = {2016},
-  publisher = {Elsevier},
-  doi = {10.1016/j.compchemeng.2015.10.010}
-}
-
 @article{gondzio-2012,
   title = {Interior point methods 25 years later},
   author = {Gondzio, Jacek},
@@ -420,14 +409,6 @@ @article{gondzio-2012
   doi = {10.1016/j.ejor.2011.09.017}
 }
 
-@inproceedings{openblas,
-  title = {{AUGEM: automatically generate high performance dense linear algebra kernels on x86 CPUs}},
-  author = {Wang, Qian and Zhang, Xianyi and Zhang, Yunquan and Yi, Qing},
-  booktitle = {Proceedings of the international conference on high performance computing, networking, storage and analysis},
-  pages = {1--12},
-  year = {2013}
-}
-
 @misc{montoison-orban-hsl-2021,
   author = {A. Montoison and D. Orban and {contributors}},
   title = {{HSL.jl}: A {J}ulia interface to the {HSL} Mathematical Software Library},
@@ -438,7 +419,7 @@ @misc{montoison-orban-hsl-2021
 }
 
 @article{chen-davis-hager-rajamanickam-2008,
-  title = {Algorithm 887: CHOLMOD, supernodal sparse Cholesky factorization and update/downdate},
+  title = {Algorithm 887: {CHOLMOD}, supernodal sparse Cholesky factorization and update/downdate},
   author = {Chen, Yanqing and Davis, Timothy A and Hager, William W and Rajamanickam, Sivasankaran},
   journal = {ACM Transactions on Mathematical Software (TOMS)},
   volume = {35},
@@ -547,3 +528,10 @@ @techreport{montoison-orban-saunders-2023
   type = {{Les Cahiers du GERAD}},
   institution = {Groupe d’études et de recherche en analyse des décisions}
 }
+
+@article{stewart1990matrix,
+  title={Matrix perturbation theory},
+  author={Stewart, Gilbert W and Sun, Ji-guang},
+  journal={(No Title)},
+  year={1990}
+}

tex/main.tex

@@ -35,7 +35,7 @@
 \DeclareMathOperator{\inertia}{inertia}
 \newcommand{\ldlt}{$\mathrm{LDL^T}$\xspace}
 \newcommand{\lblt}{$\mathrm{LBL^T}$\xspace}
-\newcommand{\llt}{$\mathrm{LL^T}$\xspace}
+\newcommand{\llt}{\text{Cholesky}\xspace}
 \newcommand{\lu}{$\mathrm{LU}$\xspace}
 \newcommand{\CG}{\textsc{Cg}\xspace}
 \newcommand{\CR}{\textsc{Cr}\xspace}
@@ -74,7 +74,6 @@
 
 % \tableofcontents
 
-
 \input{sections/introduction.tex}
 \input{sections/ipm.tex}
 \input{sections/kkt_systems.tex}
@@ -94,15 +93,14 @@ \section{Conclusion}
 Looking ahead, our future plans involve enhancing the robustness of the two condensed KKT methods, particularly focusing on stabilizing convergence for small tolerances (below $10^{-8}$).
 It is worth noting that the sparse Cholesky solver can be further customized to meet the specific requirements of the interior-point method~\cite{wright1999modified}.
 % Add a sentence about NCL on GPU?
-Enhancing the two methods on the GPU would enable the resolution of large-scale problems that are currently intractable on classical CPU architectures.
-Examples include multiperiod and security-constrained OPF problems, particularly when combined with a Schur-complement approach.
+Enhancing the two methods on the GPU would enable the resolution of large-scale problems that are currently intractable on classical CPU architectures such as multiperiod and security-constrained OPF problems.
 
 \small
 \bibliographystyle{spmpsci}
 \bibliography{biblio.bib}
 \normalsize
 \section{Acknowledgements}
-This research used resources of the Argonne Leadership Computing Facility, a U.S. Department of Energy (DOE) Office of Science user facility at Argonne National Laboratory and is based on research supported by the U.S. DOE Office of Science-Advanced Scientific Computing Research Program, under Contract No. DE-AC02-06CH11357. 
+This research used resources of the Argonne Leadership Computing Facility, a U.S. Department of Energy (DOE) Office of Science user facility at Argonne National Laboratory and is based on research supported by the U.S. DOE Office of Science-Advanced Scientific Computing Research Program, under Contract No. DE-AC02-06CH11357.
 \end{document}
 
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