Strong Convergence of Projected Subgradient Methods for Nonsmooth and Nonstrictly Convex Minimization

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A unified algorithm for solving variational inequality and fixed point problems with application to the split equality problem (2019, background): “(1.9) As an improvement on (1.9), Maingé (2008) proposed the following hybrid extragradient viscosity method which does not involve computing the projection onto the intersection Ck ∩ Qk : ⎧ ⎪⎨ ⎪⎩ yk = PC (xk − λk Axk), zk = PC (xk − λk Ayk), xk+1 = [(1 − w)I + wT ]tk, tk = zk − αk…”
Minimum-norm solution of variational inequality and fixed point problem in banach spaces (2015, background): “10 [17] Let {an} be sequences of real numbers such that there exists a subsequence {ni } of {n} such that ani < ani +1 for all i ∈ N.”
An inexact subgradient algorithm for Equilibrium Problems (2011, background): “Let us note that, condition A3 has been considered in [14] in the setting of optimization problems.”
Strong convergence theorem for a common point of solution of variational inequality and fixed point problem (2012, neutral): “[10] Let { a n } be sequences of real numbers such that there exists a subse-quence { n i } of { n } such that a n i a n i +1 for all i ∈ N .”