A Hybrid Extragradient-Viscosity Method for Monotone Operators and Fixed Point Problems

By Paul-Emile Maingé. SIAM Journal of Control and Optimization, 2008

366 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/3102676f99b1f7537c66cfe027228f21f28c3b42

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Citations in the corpus

A self adaptive inertial subgradient extragradient algorithm for variational inequality and common fixed point of multivalued mappings in Hilbert spaces (2019, background): “[20] Let {an} be a sequence of real numbers such that there exists a subsequence {ni} of {n}with ani < ani+1 for all i ∈ N.”
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…”
Iterative algorithm with self-adaptive step size for approximating the common solution of variational inequality and fixed point problems (2021, background): “In particular, such a common solution problem has application in image recovery, signal processing (see [26] and other references therein).”
Modified Tseng's extragradient methods for solving pseudo-monotone variational inequalities (2019, positive): “Following the technique in [34] we define Γn = ‖xn − p‖2 for all n ≥ 1 and let τ : N → N be a mapping defined for all n ≥ n0 (for some n0 large enough) by”
Solving the Variational Inequality Problem Defined on Intersection of Finite Level Sets (2013, background): “Assume (𝑎 𝑛 ) is a sequence of nonnegative real numbers such that where (𝛾 𝑛 ) is a sequence in (0, 1) and In this paper, inspired and encouraged by an idea in [26], we obtain the following lemma.”
An efficient iterative method for finding common fixed point and variational inequalities in Hilbert spaces (2018, methodology): “Maingé [26, Theorem 4.1]) proved that the sequence {xn}∞n=0 generated by (9) converges strongly to a solution of (4).”
Modified subgradient extragradient algorithms for variational inequality problems and fixed point problems (2018, methodology): “8 [22]: Let {an} be a sequence of nonnegative real numbers such that there exists a subsequence {anj } of {an} such that anj < anj+1 for all j ∈ N.”
On extragradient-viscosity methods for solving equilibrium and fixed point problems in a Hilbert space (2015, methodology): “4 from [18] in the previous version of this paper.”