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The Tikhonov regularization extended to equilibrium problems involving pseudomonotone bifunctions
Authors:Pham Gia Hung
Institution:
  • a Nhatrang University - 2, Nguyen Dinh Chieu, Nhatrang, Viet Nam
  • b Institute of Mathematics, VAST - 18, Hoang Quoc Viet, Hanoi, Viet Nam
  • Abstract:We extend the Tikhonov regularization method widely used in optimization and monotone variational inequality studies to equilibrium problems. It is shown that the convergence results obtained from the monotone variational inequality remain valid for the monotone equilibrium problem. For pseudomonotone equilibrium problems, the Tikhonov regularized subproblems have a unique solution only in the limit, but any Tikhonov trajectory tends to the solution of the original problem, which is the unique solution of the strongly monotone equilibrium problem defined on the basis of the regularization bifunction.
    Keywords:Equilibrium problem  Multivalued variational inequality  Tikhonov regularization  Pseudomonotonicity
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