Browsing by Author "Karahan, I."

Now showing 1 - 6 of 6

A Conjugate Gradient Algorithm for the Non-Convex Minimization Problem and Its Convergence Properties
(Taylor & Francis Ltd, 2025) Akdag, D.; Altiparmak, E.; Karahan, I.; Jolaoso, L. O.
This study introduces a new and efficient modification of the conjugate gradient algorithm for solving non-convex unconstrained optimization problems. The proposed method ensures the sufficient descent property regardless of the line search technique and is proven to be globally convergent under both Wolfe and Armijo conditions. Its numerical performance is assessed through a set of large-scale benchmark problems. The findings indicate that the proposed algorithm exhibits competitive efficiency and reliability compared to existing conjugate gradient variants. To demonstrate applicability further, the algorithm is tested on two scenarios. The first is an image restoration problem, and the second is the motion control of a 2-DOF planar robotic manipulator, where inverse kinematics is solved iteratively for trajectory tracking. The algorithm demonstrates high tracking precision and stable convergence, highlighting its theoretical soundness and potential for various optimization applications.
Convergence of SP Iterative Scheme for Three Multivalued Mappings in Hyperbolic Space
(Eudoxus Press, LLC, 2018) Gunduz, B.; Karahan, I.
The present paper aims to deal with multivalued version of SP iterative scheme to approximate a common fixed point of three multivalued nonexpansive mappings in a uniformly convex hyperbolic space and obtain strong and Δ-convergence theorems for the SP process. Our results extend some existing results in the contemporary literature. © 2018 by Eudoxus Press, LLC. All rights reserved.
An Iterative Method for Common Solution to Various Problems
(Jangjeon Mathematical Society, 2019) Karahan, I.; Khan, S.H.
In this paper, we introduce a new iterative method to find a common solution of a generalized mixed equilibrium problem, a variational inequality problem and a hierarchical fixed point problem for demicontinuous nearly nonexpansive mappings. We prove that our method converges strongly to a common solution of all above problems. It is worth noting that Main Theorem is proved without usual demiclosedness condition. As our iterative method generalizes several methods, the results here improve and extend many recent results. © 2019 Jangjeon Mathematical Society. All rights reserved.
Strong and Weak Convergence Theorems for Split Equality Generalized Mixed Equilibrium Problem
(Springer International Publishing, 2016) Karahan, I.
In this paper, we consider split equality generalized mixed equilibrium problem, which is more general than many problems such as split feasibility problem, split equality problem, split equilibrium problem, and so on. We propose a new modified algorithm to obtain strong and weak convergence theorems for split equality generalized mixed equilibrium problem for nonexpansive mappings in Hilbert spaces. Also, we give some applications to other problems. Our results extend some results in the literature. © 2016, The Author(s).
The Tseng's Extragradient Method for Semistrictly Quasimonotone Variational Inequalities
(Biemdas Academic Publishers, 2022) Rehman, H.U.; Özdemir, M.; Karahan, I.; Wairojjana, N.
In this paper, we investigate the weak convergence of an iterative method for solving classical variational inequalities problems with semistrictly quasimonotone and Lipschitz-continuous mappings in real Hilbert space. The proposed method is based on Tseng's extragradient method and uses a set stepsize rule that is dependent on the Lipschitz constant as well as a simple self-adaptive stepsize rule that is independent of the Lipschitz constant. We proved a weak convergence theorem for our method without requiring any additional projections or the knowledge of the Lipschitz constant of the involved mapping. Finally, we offer some numerical experiments that demonstrate the efficiency and benefits of the proposed method. © 2022 Journal of Applied and Numerical Optimization.
Weak and Strong Convergence Theorems for Generalized Nonexpansive Mappings
(Universitatii Al.I.Cuza din Iasi Carol I, no. 11 Iasi 700506, 2016) Khan, S.H.; Karahan, I.
We consider a class of generalized nonexpansive mappings introduced by Karapinar and seen as a generalization of Suzuki (C)-condition. We prove some weak and strong convergence theorems for approximating fixed points of such mappings under suitable conditions in uniformly convex Banach spaces. Our results generalize those of Khan and Suzuki to the case of this kind of mappings and, in turn, are related to a famous convergence theorem of Reich on nonexpansive mappings. © 2016, Universitatii Al.I.Cuza din Iasi. All rights reserved.