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A projection subgradient method for solving optimization with variational inequality constraints

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Abstract

In this paper, we propose a projection subgradient method for solving some classical variational inequality problem over the set of solutions of mixed variational inequalities. Under the conditions that \(T\) is a \(\Theta \)-pseudomonotone mapping and \(A\) is a \(\rho \)-strongly pseudomonotone mapping, we prove the convergence of the algorithm constructed by projection subgradient method. Our algorithm can be applied for instance to some mathematical programs with complementarity constraints.

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Authors and Affiliations

  1. Department of Mathematics, Sichuan Normal University, Chengdu, 610066, Sichuan, People’s Republic of China

    Fu-quan Xia & Tao Li

  2. Department of Mathematics, Sichuan University, Chengdu, 610064, Sichuan, People’s Republic of China

    Yun-zhi Zou

Authors
  1. Fu-quan Xia
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  2. Tao Li
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  3. Yun-zhi Zou
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Corresponding author

Correspondence to Yun-zhi Zou.

Additional information

This work was supported by the National Natural Science Foundation of China (11171237, 70831005), the NSF of Sichuan Education Department of China (09ZA091)

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Xia, Fq., Li, T. & Zou, Yz. A projection subgradient method for solving optimization with variational inequality constraints. Optim Lett 8, 279–292 (2014). https://doi.org/10.1007/s11590-012-0573-6

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  • DOI: https://doi.org/10.1007/s11590-012-0573-6

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