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The superiorization method with restarted perturbations for split minimization problems with an application to radiotherapy treatment planning

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  • Aragón-Artacho, Francisco J.
  • Censor, Yair
  • Gibali, Aviv
  • Torregrosa-Belén, David

Abstract

In this paper we study the split minimization problem that consists of two constrained minimization problems in two separate spaces that are connected via a linear operator that maps one space into the other. To handle the data of such a problem we develop a superiorization approach that can reach a feasible point with reduced (not necessarily minimal) objective function values. The superiorization methodology is based on interlacing the iterative steps of two separate and independent iterative processes by perturbing the iterates of one process according to the steps dictated by the other process. We include in our developed method two novel elements. The first one is the permission to restart the perturbations in the superiorized algorithm which results in a significant acceleration and increases the computational efficiency. The second element is the ability to independently superiorize subvectors. This caters to the needs of real-world applications, as demonstrated here for a problem in intensity-modulated radiation therapy treatment planning.

Suggested Citation

  • Aragón-Artacho, Francisco J. & Censor, Yair & Gibali, Aviv & Torregrosa-Belén, David, 2023. "The superiorization method with restarted perturbations for split minimization problems with an application to radiotherapy treatment planning," Applied Mathematics and Computation, Elsevier, vol. 440(C).
    • Handle: RePEc:eee:apmaco:v:440:y:2023:i:c:s0096300322007007
    DOI: 10.1016/j.amc.2022.127627
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    References listed on IDEAS

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    1. Francisco J. Aragón Artacho & Rubén Campoy, 2018. "A new projection method for finding the closest point in the intersection of convex sets," Computational Optimization and Applications, Springer, vol. 69(1), pages 99-132, January.
    2. Yair Censor & Ran Davidi & Gabor T. Herman & Reinhard W. Schulte & Luba Tetruashvili, 2014. "Projected Subgradient Minimization Versus Superiorization," Journal of Optimization Theory and Applications, Springer, vol. 160(3), pages 730-747, March.
    3. Simeon Reich & Truong Minh Tuyen, 2021. "Projection Algorithms for Solving the Split Feasibility Problem with Multiple Output Sets," Journal of Optimization Theory and Applications, Springer, vol. 190(3), pages 861-878, September.
    4. Yair Censor & Alexander J. Zaslavski, 2015. "Strict Fejér Monotonicity by Superiorization of Feasibility-Seeking Projection Methods," Journal of Optimization Theory and Applications, Springer, vol. 165(1), pages 172-187, April.
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