Self-adaptive Technique with Double Inertial Steps for Inclusion Problem on Hadamard Manifolds

doi:10.1007/s40305-024-00537-0

Abstract

Abstract: In this article, we investigate monotone and Lipschitz continuous variational inclusion problem in the settings of Hadamard manifolds. We propose a forward–backward method with a self-adaptive technique for solving variational inclusion problem. To increase the rate of convergence of our proposed method, we incorporate our iterative method with double inertial steps and establish a convergence result of our iterative method under some mild conditions. Finally, in order to illustrate the computational effectiveness of our method, some numerical examples are also discussed. The result present in this article is new in this space and extends many related results in the literature.

Key words: Variational inclusion problem, Double inertial method, Hadamard manifold, Monotone operator, Riemannian manifold

CLC Number:

47H09·49J25·65K10·90C25

Hammed Anuoluwapo Abass, Olawale Kazeem Oyewole, Kazeem Olalekan Aremu, Lateef Olakunle Jolaoso. Self-adaptive Technique with Double Inertial Steps for Inclusion Problem on Hadamard Manifolds[J]. Journal of the Operations Research Society of China, 2026, 14(3): 1038-1060.

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URL: https://www.jorsc.shu.edu.cn/EN/10.1007/s40305-024-00537-0

https://www.jorsc.shu.edu.cn/EN/Y2026/V14/I3/1038

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Self-adaptive Technique with Double Inertial Steps for Inclusion Problem on Hadamard Manifolds

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