An efficient iterative method for finding common fixed point and variational inequalities in Hilbert spaces

By Aviv Gibali, Yekini Shehu. Optimization, 2018

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ABSTRACT In this paper, we investigate the problem of finding a common solution to a fixed point problem involving demi-contractive operator and a variational inequality with monotone and Lipschitz continuous mapping in real Hilbert spaces. Inspired by the projection and contraction method and the hybrid descent approximation method, a new and efficient iterative method for solving the problem is introduced. Strong convergence theorem of the proposed method is established under standard and mild conditions. Our scheme generalizes and extends some of the existing results in the literature, and moreover, its computational effort is less per each iteration compared with related works.

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

View Paper: https://www.semanticscholar.org/paper/c145c68c70fe7ae50fc7e034574b8394f29e5ce9

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Citations in the corpus

Fast and Simple Bregman Projection Methods for Solving Variational Inequalities and Related Problems in Banach Spaces (2020, background): “Due to the importance of VIs and FPs as modelling tools in various fields such as signal processing, network resource allocation, image recovery and more, see for example [19,24,32], many authors have studied the problem of finding common elements of both problems.”