Algorithms for the Split Variational Inequality Problem

By Yair Censor, Aviv Gibali, Simeon Reich. Numerical Algorithms, 2010

707 citations recorded by the source corpus.

We propose a prototypical Split Inverse Problem (SIP) and a new variational problem, called the Split Variational Inequality Problem (SVIP), which is a SIP. It entails finding a solution of one inverse problem (e.g., a Variational Inequality Problem (VIP)), the image of which under a given bounded linear transformation is a solution of another inverse problem such as a VIP. We construct iterative algorithms that solve such problems, under reasonable conditions, in Hilbert space and then discuss special cases, some of which are new even in Euclidean space.

Subfields: Civil and Structural Engineering, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/ff73ad9e51f79cc364545e7933f22cc2a74f28fc

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Civil and Structural Engineering

1. Yekini Shehu
2. Dang Van Hieu
3. Duong Viet Thong
4. Oluwatosin Temitope Mewomo
5. Aviv Gibali
6. Rapeepan Kraikaew
7. Satit Saejung
8. Grace Nnennaya Ogwo

In Computational Theory and Mathematics

1. Dang Van Hieu
2. Oluwatosin Temitope Mewomo
3. Yekini Shehu
4. Duong Viet Thong
5. Aviv Gibali
6. Timilehin Opeyemi Alakoya
7. Lateef Olakunle Jolaoso
8. Satit Saejung

In Numerical Analysis

1. Dang Van Hieu
2. Oluwatosin Temitope Mewomo
3. Yekini Shehu
4. Duong Viet Thong
5. Aviv Gibali
6. Timilehin Opeyemi Alakoya
7. Lateef Olakunle Jolaoso
8. Adeolu Taiwo

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, methodology): “An attempt in this direction was initiated by Y. Censor et al. [13] who modified the EgM method by replacing the second projectionwith a projection onto a half-space.”
• Iterative methods for solving the generalized split common null point problem in Hilbert spaces (2020, background): “[5,6], Masad and Reich [7], Moudafi [8], Schopfer et al.”
• Split Monotone Variational Inclusions (2011, methodology): “Now, denoting by = {x which solves (6); Ax solves (7)} and using the abbreviations T := J2 λ (I − λg) and U := J1 λ (I − λf ) , based on the work of CensorGibali-Reich [1] and having in hand Theorem 2.”
• Strong Convergence of the Halpern Subgradient Extragradient Method for Solving Variational Inequalities in Hilbert Spaces (2014, methodology): “, [9–11]).”
• An iterative method for solving split monotone variational inclusion and fixed point problems (2015, positive): “Now, recall the Split Variational Inequality Problem (SVIP) introduced in [9], which is an SIP with a VIP in each one of the two spaces.”