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A generalized projection-based scheme for solving convex constrained optimization problems

Author

Listed:
  • Aviv Gibali

    (ORT Braude College)

  • Karl-Heinz Küfer

    (Fraunhofer - ITWM)

  • Daniel Reem

    (Technion - Israel Institute of Technology)

  • Philipp Süss

    (Fraunhofer - ITWM)

Abstract

In this paper we present a new algorithmic realization of a projection-based scheme for general convex constrained optimization problem. The general idea is to transform the original optimization problem to a sequence of feasibility problems by iteratively constraining the objective function from above until the feasibility problem is inconsistent. For each of the feasibility problems one may apply any of the existing projection methods for solving it. In particular, the scheme allows the use of subgradient projections and does not require exact projections onto the constraints sets as in existing similar methods. We also apply the newly introduced concept of superiorization to optimization formulation and compare its performance to our scheme. We provide some numerical results for convex quadratic test problems as well as for real-life optimization problems coming from medical treatment planning.

Suggested Citation

  • Aviv Gibali & Karl-Heinz Küfer & Daniel Reem & Philipp Süss, 2018. "A generalized projection-based scheme for solving convex constrained optimization problems," Computational Optimization and Applications, Springer, vol. 70(3), pages 737-762, July.
    • Handle: RePEc:spr:coopap:v:70:y:2018:i:3:d:10.1007_s10589-018-9991-4
    DOI: 10.1007/s10589-018-9991-4
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    References listed on IDEAS

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    1. John W. Chinneck, 2008. "Feasibility and Infeasibility in Optimization," International Series in Operations Research and Management Science, Springer, number 978-0-387-74932-7, September.
    2. Yair Censor & Wei Chen & Patrick Combettes & Ran Davidi & Gabor Herman, 2012. "On the effectiveness of projection methods for convex feasibility problems with linear inequality constraints," Computational Optimization and Applications, Springer, vol. 51(3), pages 1065-1088, April.
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    Cited by:

    1. Jason Xu & Eric C. Chi & Meng Yang & Kenneth Lange, 2018. "A majorization–minimization algorithm for split feasibility problems," Computational Optimization and Applications, Springer, vol. 71(3), pages 795-828, December.
    2. Yair Censor & Daniel Reem & Maroun Zaknoon, 2022. "A generalized block-iterative projection method for the common fixed point problem induced by cutters," Journal of Global Optimization, Springer, vol. 84(4), pages 967-987, December.
    3. Songnian He & Qiao-Li Dong, 2018. "The Combination Projection Method for Solving Convex Feasibility Problems," Mathematics, MDPI, vol. 6(11), pages 1-13, November.

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