Complexity of variants of Tseng’s modified F-B splitting and Korpelevich’s methods for generalized variational inequalities with applications to saddle point and convex optimization problems

In this paper, we consider both a variant of Tseng’s modified forward-backward splitting method and an extension of Korpelevich’s method for solving generalized variational inequalities with Lipschitz continuous operators. By showing that these methods are special cases of the hybrid proximal extragradient (HPE) method introduced by Solodov and Svaiter, we derive iteration-complexity bounds for them … Read more