Inertial self-adaptive parallel extragradient-type method for common solution of variational inequality problems

Inertial self-adaptive Bregman projection method for finite family of variational inequality problems in reflexive Banach spaces

“…(2) Suppose H = E is a real Hilbert space, then the result obtained in Jolaoso et al (2021b) becomes a corollary of our main theorem.…”

“…The most popular of these methods is the Extragradient method (EGM) which was first introduced by Korpelevich (1976) for solving the saddle point problem. The EGM is known to be characterized with some drawbacks in its use for the VIP (Jolaoso et al 2021b;Jolaoso and Aphane 2020). For instance, the EGM only converges weakly when the underlying operator is monotone.…”

“…It is known that the line-search idea uses an inner iteration which consume additional time and memory in its computation. Jolaoso et al (2021b) recently proposed a new self-adaptive technique as an improvement of the previous methods for solving the CSVIP with monotone operators in real Hilbert spaces.…”

Inertial‐like Bregman projection method for solving systems of variational inequalities

“…Let $$$ {\mathcal{K}}_i:= \mathcal{K}=\left\{x\in {l}_2:{\left\Vert x\right\Vert}_{l_2}\le 1\right\} $$$. In this experiment, we compare performance of our algorithm (IBPA) with the inertial parallel subextragradient algorithm (IPSA) proposed in Jolaoso et al [6, Algorithm 4] and modified parallel hybrid subgradient extragradient method (MPHSEM) proposed in Kitisak et al [25]. In our algorithm, we choose all parameters be the same as in Example 4.1.…”

“…This explains why a considerable research effort has been wildly devoted in both theory and applications for solving the VIP. Consequently, many researchers have been devoted to finding appropriate numerical algorithms for approximating a solution and common solution of VIP in several settings (see, e.g., earlier studies [6–9] and references therein). A classical and simplest method for solving VIP in a real Hilbert space $$$ \mathcal{H} $$$ is the projection method, which is defined by $$$ {x}_{n+1}={P}_{\mathcal{K}}\left({x}_n-\lambda \mathcal{A}{x}_n\right) $$$, where $$$ \lambda >0 $$$ is a suitable stepsize and $$$ {P}_{\mathcal{K}} $$$ is the metric (nearest point) projection from $$$ \mathcal{H} $$$ onto $$$ \mathcal{K} $$$.…”