@article{Kishimoto2017,
title = "A successive {LP} approach with {C}-{V}a{R} type constraints for {IMRT} optimization ",
journal = "Operations Research for Health Care ",
volume = "",
number = "",
pages = " - ",
year = "2017",
note = "",
issn = "2211-6923",
doi = "https://doi.org/10.1016/j.orhc.2017.09.007",
url = "https://www.sciencedirect.com/science/article/pii/S2211692316301631",
author = "Shogo Kishimoto and Makoto Yamashita",
keywords = "Intensity-modulated radiotherapy treatment",
keywords = "Fluence map optimization",
keywords = "Linear programming",
keywords = "Conditional value-at-risk ",
abstract = "Abstract In this paper, we propose a successive linear programming (LP) approach for an intensity-modulated radiotherapy treatment (IMRT) optimization. The use of \{IMRT\} enables to control the beam intensities accurately and gives more flexibility for cancer treatment plans, but finding a feasible plan that satisfies all dose-volume constraints (DVCs) requires expensive computation cost. Romeijn et al. (2003) replaced the \{DVCs\} with C-VaR (conditional Value-at-Risk) type constraints, and successfully reduced this computation cost. However, the feasible region of the \{LP\} problem was small compared to the original DVCs, therefore, their approach often failed to find a feasible plan even when the \{DVCs\} were not so stringent. In the proposed method, we integrate the C-VaR type constraints with a successive \{LP\} approach. Exploiting the solution of \{LP\} problems, we automatically detect outliers and remove them from the domain of the C-VaR type constraints. This reduces the sensitivity of the C-VaR type constraints to outliers, therefore, we can search feasible plans in a wider region than the C-VaR type constraints. We give a mathematical proof that if the optimal value of an \{LP\} problem in the proposed method is non-positive, the corresponding optimal solution satisfies all the DVCs. From a numerical experiment on test data sets, we observed that the proposed method found feasible solutions more appropriately than existing successive \{LP\} approaches. Moreover, the proposed method required fewer \{LP\} problems, and this was reflected in a short computation time. "
}

@article{yang2017arc,
  title={An arc-search $\mathcal{O}(n{L})$ infeasible-interior-point algorithm for linear programming},
  author={Yang, Yaguang and Yamashita, Makoto},
  journal={Optimization Letters},
  pages={1--18},
  year={2017},
  publisher={Springer}
}

@article{safarina2017conic,
  title={Conic relaxation approaches for equal deployment problems},
  author={Safarina, Sena and Moriguchi, Satoko and Mullin, Tim J and Yamashita, Makoto},
  journal={arXiv preprint arXiv:1703.03155},
  year={2017}
}