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An explicit extragradient algorithm for equilibrium problems on Hadamard manifolds. (English) Zbl 1476.65085

Summary: In this paper, we investigate a new extragradient algorithm for solving pseudomonotone equilibrium problems on Hadamard manifolds. Our algorithm uses a variable stepsize, which is updated at each iteration and based on some previous iterates. The convergence analysis of the proposed algorithm is discussed under mild assumptions. In the case where the equilibrium bifunction is strongly pseudomonotone, the \(R\)-linear rate of convergence of the new algorithm is formulated. A fundamental experiment is provided to illustrate the numerical behavior of the algorithm.

MSC:

65J15 Numerical solutions to equations with nonlinear operators
54H25 Fixed-point and coincidence theorems (topological aspects)
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
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