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A proximal point algorithm based on decomposition method for cone constrained multiobjective optimization problems

Author

Listed:
  • Jiawei Chen

    (Southwest University)

  • Qamrul Hasan Ansari

    (Aligarh Muslim University
    King Fahd University of Petroleum & Minerals)

  • Yeong-Cheng Liou

    (Cheng Shiu University)

  • Jen-Chih Yao

    (China Medical University
    China Medical University Hospital, China Medical University)

Abstract

By using auxiliary principle technique, a new proximal point algorithm based on decomposition method is suggested for computing a weakly efficient solution of the constrained multiobjective optimization problem (MOP) without assuming the nonemptiness of its solution set. The optimality conditions for (MOP) are derived by the Lagrangian function of its subproblem and corresponding mixed variational inequality. Some basic properties and convergence results of the proposed method are established under some mild assumptions. As an application, we employ the proposed method to solve a split feasibility problem. Finally, numerical results are also presented to illustrate the feasibility of the proposed algorithm.

Suggested Citation

  • Jiawei Chen & Qamrul Hasan Ansari & Yeong-Cheng Liou & Jen-Chih Yao, 2016. "A proximal point algorithm based on decomposition method for cone constrained multiobjective optimization problems," Computational Optimization and Applications, Springer, vol. 65(1), pages 289-308, September.
    • Handle: RePEc:spr:coopap:v:65:y:2016:i:1:d:10.1007_s10589-016-9840-2
    DOI: 10.1007/s10589-016-9840-2
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    References listed on IDEAS

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    5. 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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