On the convergence of descent methods for monotone variational inequalities

Recently, Zhu and Marcotte [15] established the convergence of a modified descent algorithm for monotone variational inequalities. Using algorithmic equivalence results due to Patriksson [10, 11] and Larsson and Patriksson [7], we show that this convergence result may be used to establish the convergence of slightly modified versions of the classical successive approximation algorithms of Dafermos [2] and Cohen [1], and of the descent algorithms of Wu et al. [14], Patriksson [10, 11], and Larsson and Patriksson [7], under assumptions that are both much milder and much easier to verify than those for their original statements.