Convergence Analysis of the Generalized Alternating Direction Method of Multipliers with Logarithmic–Quadratic Proximal Regularization

We consider combining the generalized alternating direction method of multipliers, proposed by Eckstein and Bertsekas, with the logarithmic–quadratic proximal method proposed by Auslender, Teboulle, and Ben-Tiba for solving a variational inequality with separable structures. For the derived algorithm, we prove its global convergence and establish its worst-case convergence rate measured by the iteration complexity in both the ergodic and nonergodic senses.