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

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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.

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Acknowledgments

The authors are grateful to the associated editor and the three anonymous referees for their valuable comments and suggestions to improve the first draft of this paper. This research was carried out during the visit of Jiawei Chen to National Sun Yat-Sen University, Kaohsiung in July 2014. The first author was partially supported by the Natural Science Foundation of China (11401487), the Fundamental Research Funds for the Central Universities (SWU113037, XDJK2014C073). The third author was partially supported by the grant MOST 101-2628-E-230-001-MY3 and MOST 101-2622-E-230-005-CC3. The fourth author was partially supported by MOST 103-2923 E-039-001-MY3.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Southwest University, Chongqing, 400715, People’s Republic of China

    Jiawei Chen

  2. Department of Mathematics, Aligarh Muslim University, Aligarh, India

    Qamrul Hasan Ansari

  3. Department of Mathematics and Statistics, King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia

    Qamrul Hasan Ansari

  4. Department of Information Management, Cheng Shiu University, Kaohsiung, 833, Taiwan

    Yeong-Cheng Liou

  5. Center for General Education, China Medical University, Taichung, 40402, Taiwan

    Jen-Chih Yao

  6. Research Center for Interneural Computing, China Medical University Hospital, China Medical University, Taichung, 40402, Taiwan

    Jen-Chih Yao

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  1. Jiawei Chen
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  2. Qamrul Hasan Ansari
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  3. Yeong-Cheng Liou
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  4. Jen-Chih Yao
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Correspondence to Jen-Chih Yao.

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Chen, J., Ansari, Q.H., Liou, YC. et al. A proximal point algorithm based on decomposition method for cone constrained multiobjective optimization problems. Comput Optim Appl 65, 289–308 (2016). https://doi.org/10.1007/s10589-016-9840-2

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