IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v70y2018i3d10.1007_s10589-018-9991-4.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10589-018-9991-4
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10589-018-9991-4?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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, December.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. Songnian He & Qiao-Li Dong, 2018. "The Combination Projection Method for Solving Convex Feasibility Problems," Mathematics, MDPI, vol. 6(11), pages 1-13, November.
    3. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jérémy Omer & Michael Poss, 2021. "Identifying relatively irreducible infeasible subsystems of linear inequalities," Annals of Operations Research, Springer, vol. 304(1), pages 361-379, September.
    2. Peichao Duan & Xubang Zheng & Jing Zhao, 2018. "Strong Convergence Theorems of Viscosity Iterative Algorithms for Split Common Fixed Point Problems," Mathematics, MDPI, vol. 7(1), pages 1-14, December.
    3. Xianfu Wang & Xinmin Yang, 2015. "On the Existence of Minimizers of Proximity Functions for Split Feasibility Problems," Journal of Optimization Theory and Applications, Springer, vol. 166(3), pages 861-888, September.
    4. 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.
    5. Briec, Walter & Kerstens, Kristiaan & Prior, Diego & Van de Woestyne, Ignace, 2010. "Tangency capacity notions based upon the profit and cost functions: A non-parametric approach and a general comparison," Economic Modelling, Elsevier, vol. 27(5), pages 1156-1166, September.
    6. Laurence Smith & John Chinneck & Victor Aitken, 2013. "Improved constraint consensus methods for seeking feasibility in nonlinear programs," Computational Optimization and Applications, Springer, vol. 54(3), pages 555-578, April.
    7. Stéphane Chrétien & Pascal Bondon, 2020. "Projection Methods for Uniformly Convex Expandable Sets," Mathematics, MDPI, vol. 8(7), pages 1-19, July.
    8. Chin How Jeffrey Pang, 2019. "Dykstra’s Splitting and an Approximate Proximal Point Algorithm for Minimizing the Sum of Convex Functions," Journal of Optimization Theory and Applications, Springer, vol. 182(3), pages 1019-1049, September.
    9. Brendan O’Donoghue & Eric Chu & Neal Parikh & Stephen Boyd, 2016. "Conic Optimization via Operator Splitting and Homogeneous Self-Dual Embedding," Journal of Optimization Theory and Applications, Springer, vol. 169(3), pages 1042-1068, June.
    10. Wenma Jin & Yair Censor & Ming Jiang, 2016. "Bounded perturbation resilience of projected scaled gradient methods," Computational Optimization and Applications, Springer, vol. 63(2), pages 365-392, March.
    11. Erick Moreno-Centeno & Richard M. Karp, 2013. "The Implicit Hitting Set Approach to Solve Combinatorial Optimization Problems with an Application to Multigenome Alignment," Operations Research, INFORMS, vol. 61(2), pages 453-468, April.
    12. Kadziński, Miłosz & Labijak, Anna & Napieraj, Małgorzata, 2017. "Integrated framework for robustness analysis using ratio-based efficiency model with application to evaluation of Polish airports," Omega, Elsevier, vol. 67(C), pages 1-18.
    13. Canan Ulu & Murat Köksalan, 2014. "An interactive approach to multicriteria sorting for quasiconcave value functions," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(6), pages 447-457, September.
    14. Wiesława T. Obuchowska, 2015. "Irreducible Infeasible Sets in Convex Mixed-Integer Programs," Journal of Optimization Theory and Applications, Springer, vol. 166(3), pages 747-766, September.
    15. Nikolaos P. Theodorakatos & Miltiadis Lytras & Rohit Babu, 2020. "Towards Smart Energy Grids: A Box-Constrained Nonlinear Underdetermined Model for Power System Observability Using Recursive Quadratic Programming," Energies, MDPI, vol. 13(7), pages 1-17, April.
    16. Wiesława Obuchowska, 2010. "Minimal infeasible constraint sets in convex integer programs," Journal of Global Optimization, Springer, vol. 46(3), pages 423-433, March.
    17. Howard Heaton & Yair Censor, 2019. "Asynchronous sequential inertial iterations for common fixed points problems with an application to linear systems," Journal of Global Optimization, Springer, vol. 74(1), pages 95-119, May.
    18. Paulo Oliveira, 2014. "A strongly polynomial-time algorithm for the strict homogeneous linear-inequality feasibility problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 80(3), pages 267-284, December.
    19. Oliver Bastert & Benjamin Hummel & Sven de Vries, 2010. "A Generalized Wedelin Heuristic for Integer Programming," INFORMS Journal on Computing, INFORMS, vol. 22(1), pages 93-107, February.
    20. Barbaros Yet & Ceren Tuncer Şakar, 2020. "Estimating criteria weight distributions in multiple criteria decision making: a Bayesian approach," Annals of Operations Research, Springer, vol. 293(2), pages 495-519, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:coopap:v:70:y:2018:i:3:d:10.1007_s10589-018-9991-4. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.