Browsing by Author "Shikher Sharma"

Now showing 1 - 6 of 6

A derivative free projection method for the singularities of vector fields with convex constraints on Hadamard manifolds
(Taylor and Francis Ltd., 2024) D.R. Sahu; Shikher Sharma
The objective of this paper is to introduce a derivative free projection method designed to find the singularities of pseudomonotone vector fields with convex constraints on Hadamard manifolds. This innovative approach combines the hyperplane projection method with a novel search direction. The global convergence of the proposed method is established under certain conditions. Our method improves some existing results in the literature on Hadamard manifolds. Additionally, illustrative numerical examples are provided to demonstrate the practical efficacy of our method. © 2024 Informa UK Limited, trading as Taylor & Francis Group.
A derivative free projection method for the singularities of vector fields with convex constraints on Hadamard manifolds
(Taylor and Francis Ltd., 2025) Dayaram Sahu; Shikher Sharma
The objective of this paper is to introduce a derivative free projection method designed to find the singularities of pseudomonotone vector fields with convex constraints on Hadamard manifolds. This innovative approach combines the hyperplane projection method with a novel search direction. The global convergence of the proposed method is established under certain conditions. Our method improves some existing results in the literature on Hadamard manifolds. Additionally, illustrative numerical examples are provided to demonstrate the practical efficacy of our method. © 2024 Informa UK Limited, trading as Taylor & Francis Group.
Accelerated iterative splitting methods on Hadamard manifolds
(Taylor and Francis Ltd., 2025) Dayaram Sahu; Shikher Sharma; Jenchih Yao; Xiaopeng Zhao
This paper aims to solve the monotone inclusion problem, minimization problem of multiple summands and the generalized Heron problem. We present an innovative approach, the modified normal S-iteration method, designed to approximate common fixed points of nearly nonexpansive sequences and families of operators via the property (Formula presented.). Some deductions of our results improve some existing results in the literature. To show the applicability of our result, we give application to the inclusion problem via forward–backward splitting method version of our algorithm and minimization problem via Douglas–Rachford splitting method version of our algorithm. To demonstrate the practical utility of the algorithm, we apply it to the generalized Heron problem. © 2024 Informa UK Limited, trading as Taylor & Francis Group.
Accelerated iterative splitting methods on Hadamard manifolds
(Taylor and Francis Ltd., 2024) D.R. Sahu; Shikher Sharma; J.C. Yao; Xiaopeng Zhao
This paper aims to solve the monotone inclusion problem, minimization problem of multiple summands and the generalized Heron problem. We present an innovative approach, the modified normal S-iteration method, designed to approximate common fixed points of nearly nonexpansive sequences and families of operators via the property (Formula presented.). Some deductions of our results improve some existing results in the literature. To show the applicability of our result, we give application to the inclusion problem via forward–backward splitting method version of our algorithm and minimization problem via Douglas–Rachford splitting method version of our algorithm. To demonstrate the practical utility of the algorithm, we apply it to the generalized Heron problem. © 2024 Informa UK Limited, trading as Taylor & Francis Group.
Applications of a variable anchoring iterative method to equation and inclusion problems on Hadamard manifolds
(Elsevier B.V., 2024) D.R. Sahu; Ariana Pitea; Shikher Sharma; Amit Kumar Singh
In this paper, we introduce a new iterative technique with a variable anchoring operator for reckoning the solution of a variational inequality problem over the set of the common fixed points of a nearly nonexpansive sequence of operators in the framework of Hadamard manifolds. We also establish a convergence result on the proposed algorithm for approximating a solution of the problem, under suitable assumptions. We apply our results for finding the solutions of a system of nonlinear equations, and of inclusion problems to support their utility. Our work improves results in the recent literature. Numerical simulations are given for a better understanding of the effectiveness of our outcomes. © 2024 Elsevier B.V.
The s-iterative techniques on hadamard manifolds and applications
(Biemdas Academic Publishers, 2020) D.R. Sahu; Feeroz Babu; Shikher Sharma
In this paper, we develop S-iterative techniques in terms of exponential mappings for finding fixed points of nonexpansive mappings on Hadamard manifolds. To demonstrate numerical applicability, we show our proposed methods are faster than the existing results in the literature. For the applications, we focus on the common singularities of set-valued monotone vector fields and convex feasibility problems. © 2020 Journal of Applied and Numerical Optimization.