A New Linesearch Algorithm for Split Equilibrium Problems


In this paper, we propose a new algorithm for solving a split equilibrium problem involving nonmonotone and monotone equilibrium bifunctions in real Hilbert spaces by using a shrinking projection method with a general Armijo line search rule on the ε-subdifferential. We obtain a strong convergence theorem for the new algorithm.

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The first author would like to thank the Thailand Research Fund through the Royal Golden Jubilee Ph.D. Program and Naresuan University for supporting his research via Grant No. PHD/0032/2555.

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Correspondence to Somyot Plubtieng.

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Dedicated to Professor Hoang Tuy

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Yuying, T., Plubtieng, S. A New Linesearch Algorithm for Split Equilibrium Problems. Acta Math Vietnam 45, 397–409 (2020). https://doi.org/10.1007/s40306-020-00361-7

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  • Split equilibrium problem
  • Line search rule
  • Projected methods
  • Strong convergence

Mathematics Subject Classification (2010)

  • 47H09
  • 47J25
  • 65K10
  • 65K15
  • 90C99