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An Armijo-type method for pseudomonotone equilibrium problems and its applications. (English) Zbl 1285.65040

The authors present a new algorithm for solving equilibrium problems, where the underlying bifunctions are pseudomonotone and not necessarily Lipschitz-type continuous. The algorithm is based on the auxiliary problem principle and the Armijo-type linesearch techniques. Convergence properties of the proposed algorithms are established, among them the global convergence is proved under few assumptions. Applications to generalized variational inequalities and some numerical results are reported to evaluate the algorithm.

MSC:

65K15 Numerical methods for variational inequalities and related problems
49J40 Variational inequalities
49M25 Discrete approximations in optimal control
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