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An inertial subgradient-type method for solving single-valued variational inequalities and fixed point problems

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Abstract

In this paper, we introduce an inertial subgradient-type algorithm to find the common element of fixed point set of a family of nonexpansive mappings and the solution set of the single-valued variational inequality problem. Under the assumption that the mapping is monotone and Lipschitz continuous, we show that the sequence generated by our algorithm converges strongly to some common element of the fixed set and the solution set. Moreover, preliminary numerical experiments are also reported.

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Funding

This work is partially supported by the National Natural Science Foundation of China (No. 11771350), Basic and Advanced Research Project of CQ CSTC (No. cstc2016jcyjA0163), Science and Technology Project of Chongqing Municipal Education Committee of China (No. KJ1600433), and Chongqing Research and Innovation Project of Graduate Students (No. CYS16173).

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Authors and Affiliations

  1. School of Science, Chongqing University of Posts and Telecommunications, Chongqing, China

    Lixin Zhang, Changjie Fang & Shenglan Chen

  2. Key Lab of Intelligent Analysis and Decision on Complex Systems, Chongqing University of Posts and Telecommunications, Chongqing, 400065, China

    Changjie Fang

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  1. Lixin Zhang
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  2. Changjie Fang
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  3. Shenglan Chen
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Correspondence to Changjie Fang.

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Zhang, L., Fang, C. & Chen, S. An inertial subgradient-type method for solving single-valued variational inequalities and fixed point problems. Numer Algor 79, 941–956 (2018). https://doi.org/10.1007/s11075-017-0468-9

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  • DOI: https://doi.org/10.1007/s11075-017-0468-9

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