A quasi-Newton type method for equilibrium problems

In this work, we develop a quasi-Newton-type method for equilibrium problems based on the proximal Newton-type structure given in Santos et al. (Optimization Letters 12(5), 997-1009, 2018). We consider a family of matrices verifying a bounded deterioration property. We prove that the sequence generated by the algorithm is well defined and under suitable assumptions we establish the linear convergence of the algorithm. Numerical experiments are reported.