Proximal and Contraction method with Relaxed Inertial and Correction Terms for Solving Mixed Variational Inequality Problems

Chidi Elijah Nwakpa; Austine Efut Ofem; Kalu Okam Okorie; Chinedu Izuchukwu; Chibueze Christian Okeke

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arXiv · 2511.18652

Proximal and Contraction method with Relaxed Inertial and Correction Terms for Solving Mixed Variational Inequality Problems

Chidi Elijah Nwakpa·Austine Efut Ofem·Kalu Okam Okorie·Chinedu Izuchukwu·Chibueze Christian Okeke

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Abstract

We propose in this paper a proximal and contraction method for solving a convex mixed variational inequality problem in a real Hilbert space. To accelerate the convergence of our proposed method, we incorporate an inertial extrapolation term, two correction terms, and a relaxation technique. We therefore obtain a weak convergence result under some mild assumptions. Finally, we present numerical examples to practically demonstrate the effectiveness of the relaxation technique, the inertial extrapolation term, and the correction terms in our proposed method.

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Chidi Elijah Nwakpa, Austine Efut Ofem, Kalu Okam Okorie, Chinedu Izuchukwu, Chibueze Christian Okeke. 2025-11-23. Proximal and Contraction method with Relaxed Inertial and Correction Terms for Solving Mixed Variational Inequality Problems. https://arxiv.org/abs/2511.18652

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