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The deepest event cuts in risk-averse optimization with application to radiation therapy design

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Abstract

Our study is motivated by radiation therapy design for cancer treatment. We consider large-scale problems with stochastic order constraints. We establish a general result about the form of the deepest cuts associated with events of positive probability which are used in the numerical approximation of the functional constraints. An efficient method using the deepest cuts is proposed for the numerical solution of problems with second-order dominance constraints and increasing convex order constraints. We the propose a new methodology for the radiation-therapy design for cancer treatment. We introduce a risk-averse optimization problem with two types of stochastic order relations and with coherent measures of risk and consider the effect of the risk models in three versions of the problem formulation. Additionally, we propose a method that creates flexible (floating) benchmark distributions when benchmark distributions are not given apriori or when the provided distributions lead to infeasibility. We devise a numerical method using floating benchmarks for solving the proposed risk-averse optimization models for radiation therapy design. The models and methods are verified by using clinical data confirming the viability of the proposed methodology and its efficiency.

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Data availibility

The dataset used in the current study is not publicly available as it contains clinical data.

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Acknowledgements

The authors express their gratitude to Dr. Ning J. Yue, Department of Radiation Oncology, The Rutgers University Robert–Wood–Johnson Medical School, for kindly providing us with clinical data for the experiments. We are also grateful to the three anonymous referees whose critics helped improve the paper.

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Author notes

  1. Constantine A. Vitt, Darinka Dentcheva, Andrzej Ruszczyński, and Nolan Sandberg have contributed equally to this work.

Authors and Affiliations

  1. Department of Mathematical Sciences, Stevens Institute of Technology, Hoboken, NJ, 07030, USA

    Constantine A. Vitt & Darinka Dentcheva

  2. Department of Management Science and Information Systems, Rutgers University, Piscataway, NJ, 08854, USA

    Andrzej Ruszczyński

  3. Facebook, San Francisco, CA, USA

    Nolan Sandberg

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  1. Constantine A. Vitt
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  2. Darinka Dentcheva
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  4. Nolan Sandberg
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Correspondence to Darinka Dentcheva.

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This paper is dedicated to Asen Dontchev, with gratitude for his mentorship and in appreciation of his fundamental contributions to the theory of optimization and control.

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Vitt, C.A., Dentcheva, D., Ruszczyński, A. et al. The deepest event cuts in risk-averse optimization with application to radiation therapy design. Comput Optim Appl 86, 1347–1372 (2023). https://doi.org/10.1007/s10589-023-00531-x

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