An adaptive bregman proximal gradient algorithm for solving generalized variational inequalities with applications

In this paper, we introduce a Bregman-type proximal gradient algorithm with a new choice of adaptive stepsize for solving the generalized variational inequalities in finite-dimensional Hilbert spaces. We also proved some convergence results and the linear rate of convergence of the proposed method under mild conditions. More so, we provided some numerical implementation of the algorithm on three important problems namely, server placement problem, adversarial Gaussian communication problem and the Cournot competition model in oligopolistic markets equilibrium. The numerical results indicate that the proposed method is competitive with existing approaches, achieving a favourable balance between accuracy and computational efficiency across the tested problems.