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

Author

Listed:
  • Constantine A. Vitt

    (Stevens Institute of Technology)

  • Darinka Dentcheva

    (Stevens Institute of Technology)

  • Andrzej Ruszczyński

    (Rutgers University)

  • Nolan Sandberg

    (Facebook)

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.

Suggested Citation

  • Constantine A. Vitt & Darinka Dentcheva & Andrzej Ruszczyński & Nolan Sandberg, 2023. "The deepest event cuts in risk-averse optimization with application to radiation therapy design," Computational Optimization and Applications, Springer, vol. 86(3), pages 1347-1372, December.
  • Handle: RePEc:spr:coopap:v:86:y:2023:i:3:d:10.1007_s10589-023-00531-x
    DOI: 10.1007/s10589-023-00531-x
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    References listed on IDEAS

    as
    1. Eva Lee & Tim Fox & Ian Crocker, 2003. "Integer Programming Applied to Intensity-Modulated Radiation Therapy Treatment Planning," Annals of Operations Research, Springer, vol. 119(1), pages 165-181, March.
    2. Ogryczak, Wlodzimierz & Ruszczynski, Andrzej, 1999. "From stochastic dominance to mean-risk models: Semideviations as risk measures," European Journal of Operational Research, Elsevier, vol. 116(1), pages 33-50, July.
    3. Gastwirth, Joseph L, 1971. "A General Definition of the Lorenz Curve," Econometrica, Econometric Society, vol. 39(6), pages 1037-1039, November.
    4. Dentcheva, Darinka & Martinez, Gabriela, 2012. "Two-stage stochastic optimization problems with stochastic ordering constraints on the recourse," European Journal of Operational Research, Elsevier, vol. 219(1), pages 1-8.
    5. H. Edwin Romeijn & Ravindra K. Ahuja & James F. Dempsey & Arvind Kumar, 2006. "A New Linear Programming Approach to Radiation Therapy Treatment Planning Problems," Operations Research, INFORMS, vol. 54(2), pages 201-216, April.
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    Cited by:

    1. William W. Hager & R. Tyrrell Rockafellar & Vladimir M. Veliov, 2023. "Preface to Asen L. Dontchev Memorial Special Issue," Computational Optimization and Applications, Springer, vol. 86(3), pages 795-800, December.

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