A proximal Newton-type method for equilibrium problems

In this work we extend the method considered by von Heusinger et al. (Math Program 132(1):99-123, 2012) to the setting of equilibrium problems. Moreover, we introduce a family of auxiliary bifunctions containing that one used by them. We prove that the method is locally convergent and we establish the superlinear/quadratic convergence of the algorithm to a solution of the problem under suitable assumptions. An application of the proposed method to multiobjective optimization problems is considered. Some preliminary numerical results are reported showing the performance of our algorithm.