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From progressive decoupling of linkages in variational inequalities to fixed-point problems

. Based on a very recent work by R. T. Rockafellar and the Yosida approximation, we propose a regularization approach of the idea and the associated notions presented in [16] (see also [17]). Next, we develop a similar analysis for ﬁxed-point problems. In this setting, we introduce various elicitation notions that permit us to go beyond the limitation of the usual assumptions of the pseudo-contraction or the ﬁrm non-expansiveness, and we present the related progressive decoupling algorithms. Their convergence properties are investigated under global elicitability assumptions and an application to decomposition and splitting problems is also brieﬂy mentioned.