Iterative Algorithms for Variational Inequalities and Related Optimization Problems

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E: Applied Mathematics".

Deadline for manuscript submissions: 30 September 2026 | Viewed by 674

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Guest Editor
National School of Applied Sciences, ENSA, Ibn Zohr University, Agadir BP 1136, Morocco
Interests: applied and computational mathematics optimization; iterative methods; variational inequalities; optimization algorithms
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Special Issue Information

Dear Colleagues,

Variational inequality theory constitutes a significant branch of nonlinear analysis. It provides a unified framework for studying a wide range of problems arising in physics, engineering, economics, and optimization. In recent years, the development of efficient iterative algorithms to solve variational inequalities, particularly in the context of fixed-point problems and split feasibility problems, has attracted considerable attention.

The primary objective of this Special Issue was to collect original research articles and comprehensive reviews that reflect the latest advances in iterative schemes for solving variational inequalities involving monotone and accretive operators in Hilbert and Banach spaces.

Dr. Abdellah Bnouhachem
Guest Editor

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Keywords

  • variational inequalities
  • split feasibility problem
  • generalized mixed equilibrium problem
  • fixed point problem
  • iterative algorithms

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Published Papers (1 paper)

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Research

21 pages, 635 KB  
Article
A Hybrid Projection Extragradient Method for Variational Inequality and Hierarchical Fixed-Point Problems
by Rehan Ali, Monairah Alansari and Mohammad Farid
Mathematics 2026, 14(9), 1431; https://doi.org/10.3390/math14091431 - 24 Apr 2026
Viewed by 340
Abstract
This study proposes a new strongly convergent iterative framework obtained by combining a Krasnosel’skiǐ–Mann type subgradient extragradient process with a hybrid projection strategy and an inertial extrapolation mechanism. The method is applied to address hierarchical fixed-point problems (HFPPs) for nonexpansive and quasi-nonexpansive mappings [...] Read more.
This study proposes a new strongly convergent iterative framework obtained by combining a Krasnosel’skiǐ–Mann type subgradient extragradient process with a hybrid projection strategy and an inertial extrapolation mechanism. The method is applied to address hierarchical fixed-point problems (HFPPs) for nonexpansive and quasi-nonexpansive mappings as well as variational inequality problems (VIPs) involving a pseudomonotone operator in real Hilbert spaces. The proposed scheme employs step sizes that are restricted by the inverse of the Lipschitz constant of the underlying cost operator. Strong convergence of the iterates is achieved under mild hypotheses on the inertial parameter and control sequences. The method is further applied to problems arising in optimization and monotone operator theory. The results show that the proposed framework generalizes and integrates a number of existing approaches while offering improved computational performance. Full article
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