Sep 2026· Journal of Advances in Optimization Theory· Vol 2, pp. 32-57· 0 citations· 45 references
Abstract
In this paper, we combine double inertial extrapolation with viscosity techniques to propose a novel iterative algorithm that finds a common solution to a generalized mixed equilibrium problem, a split variational inclusion problem, and a common fixed point constraint involving two nonexpansive operators in real Hilbert spaces. Distinct from existing methods, our algorithm features a self-adaptive step size that operates without prior knowledge of the operator norm. Additionally, we introduce a relaxed parameter condition for the inertial parameter, eliminating the need to estimate the Lipschitz constant. We establish the strong convergence of the proposed scheme under mild assumptions. Finally, a numerical example is provided to demonstrate the effectiveness and computational efficiency of the proposed algorithm.
This study aims to propose a self-adaptive viscosity-type algorithm with inertial effects to find the common solutions of the split mixed equilibrium, split variational inclusion and common fixed point problems associated with nonexpansive mappings. It is worth mentioning that the step size employed in this algorithm i...
Muhammad Waseem Asghar, Mujahid Abbas· Symmetry· 0 citations
In this paper, we propose a viscosity-type double inertial algorithm with self-adaptive stepsizes for solving non-monotone variational inequality problems involving uniformly continuous operators in real Hilbert spaces. The proposed method combines viscosity approximation and double inertial extrapolation techniques wi...
O. Onifade, A. E. Ofem, S. A. Kajola et al.· Annali dell?Università di Fe...· 0 citations
In this paper, we introduce a novel two-step iterative algorithm based on a double inertial subgradient extragradient method for solving non-monotone variational inequality problems in reflexive Banach spaces. Without imposing any monotonicity conditions on the cost operator, we establish strong convergence of the prop...
G. Ugwunnadi, Jacob Ashiwere Abuchu, Abdul Rahim Khan et al.· Journal of Advances in Optim...· 0 citations
In this work, we introduce a novel modified inertial iterative algorithm for solving bilevel
equilibrium problems involving pseudomonotone bifunctions in real Hilbert spaces. Theproposed scheme
incorporates a self-adaptive step-size strategy, eliminating the need for prior knowledge of Lipschitz type
constants and enha...
Loms Matto Ayuba, E. Mbah, F. U. Ogbuisi et al.· Optimization Eruditorum· 0 citations
We introduce and analyze a two-step inertial viscosity-type algorithm for approximating a common solution of a generalized mixed equilibrium problem and the fixed-point problems associated with a family of quasi-nonexpansive mappings in a real Hilbert space. The generalized mixed equilibrium model contains a monotone o...
