<p>We combine Korpelevich’s extragradient method with Tseng’s extragradient method which has double self-adaptive processes and inertial extrapolation step to solve variational inequality problems in reflexive Banach spaces. Under mild conditions imposed on the parameters, we obtain strong convergence of the sequence generated by our new method. At last, some numerical examples are listed to demonstrate the performance of the proposed algorithm.</p>

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A Bregman Projection Algorithm Combining Korpelevich’s Extragradient Method With Tseng’s Extragradient Method for Solving Variational Inequality Problems

  • Shaotao Hu,
  • Yuanheng Wang,
  • Zhongbing Xie,
  • Yuchao Tang,
  • Qiao-Li Dong

摘要

We combine Korpelevich’s extragradient method with Tseng’s extragradient method which has double self-adaptive processes and inertial extrapolation step to solve variational inequality problems in reflexive Banach spaces. Under mild conditions imposed on the parameters, we obtain strong convergence of the sequence generated by our new method. At last, some numerical examples are listed to demonstrate the performance of the proposed algorithm.