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In this work, a new algorithm is suggested to solve the variational inequality problems for Lipschitz continuous and monotone operators and the fixed point problems for quasi‐nonexpansive operators. This algorithm… Click to show full abstract
In this work, a new algorithm is suggested to solve the variational inequality problems for Lipschitz continuous and monotone operators and the fixed point problems for quasi‐nonexpansive operators. This algorithm is constructed based on the inertial subgradient extragradient method. In addition, a strong convergence theorem for this algorithm is obtained under some extra conditions. Furthermore, an application to a signal recovery in compressed sensing problem is shown as a numerical example of the algorithm. Additionally, another example in an infinite‐dimensional space is given.
Journal Title: Mathematical Methods in the Applied Sciences
Year Published: 2021
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