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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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    1. Bingsheng He & Xiaoming Yuan & Wenxing Zhang, 2013. "A customized proximal point algorithm for convex minimization with linear constraints," Computational Optimization and Applications, Springer, vol. 56(3), pages 559-572, December.
    2. Thai Chuong & Jen-Chih Yao, 2013. "Fréchet subdifferentials of efficient point multifunctions in parametric vector optimization," Journal of Global Optimization, Springer, vol. 57(4), pages 1229-1243, December.
    3. 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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    5. Jia Chen & Yeol Cho & Jong Kim & Jun Li, 2011. "Multiobjective optimization problems with modified objective functions and cone constraints and applications," Journal of Global Optimization, Springer, vol. 49(1), pages 137-147, January.
    6. J. Li & S. Q. Feng & Z. Zhang, 2013. "A Unified Approach for Constrained Extremum Problems: Image Space Analysis," Journal of Optimization Theory and Applications, Springer, vol. 159(1), pages 69-92, October.
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