Split Monotone Variational Inclusions

By Abdellatif Moudafi. Journal of Optimization Theory and Applications, 2011

459 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/5843f314fb6fef9c952ff86954d7c475196e9ae3

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Citations in the corpus

Iterative approximation of a common solution of a split generalized equilibrium problem and a fixed point problem for nonexpansive semigroup (2013, methodology): “SEP (3)-(4) includes the split variational inequality problem, split zero problem, and split feasibility problem (see, for instance, [7-12]).”
The Split Common Null Point Problem (2011, methodology): “Another related split problem is the Split Common Fixed Point Problem (SCFPP), first introduced in Euclidean spaces in [25] and later studied by Moudafi [42] in Hilbert spaces.”
Parallel Extragradient-Proximal Methods for Split Equilibrium Problems (2015, background): “1) and its special cases have been recieved a lot of attention by many authors and some methods for solving them can be found, for instance, in [8,11,12,13,14,17,19,20,22,24,25,26,30,32].”
An inertial method for solving generalized split feasibility problems over the solution set of monotone variational inclusions (2020, methodology): “3: We also like to mention that the results in [1,15,30,46,47] may not be applicable to the LASSO problem (60) since ∇F̃ (where ∇F̃(x) = D∗(Dx − y)), may generally not be an inverse strongly monotone operator.”
Weak and Strong Convergence of Algorithms for the Split Common Null Point Problem (2011, background): “Remark 3.3 Observe that in Theorem 3.2 we assume that γ ∈ (0, 2/L), while in [20, Theorem 6.3], γ is assumed to be in (0, 1/L), which obviously was a more restrictive assumption.”
An iterative method for solving split monotone variational inclusion and fixed point problems (2015, unknown): “Furthermore, we know that (see, e.g., Moudafi [23]) 0 ∈ f1(x∗) + B1(x∗) ⇔ x∗ = J B1λ (x∗ − λ f1(x∗)), and 0 ∈ f2(y∗) + B2(y∗) ⇔ y∗ = J B2λ (y∗ − λ f2(y∗)), where J B1λ := (I−λB1)−1 is the resolvent of B1 of parameterλ > 0,which is a nonexpansive mapping and everywhere defined on H1 and J B2 λ := (I ”