Accelerated Self-Adaptive Method for Solving Nonsmooth Convex Minimization Problem in Real Hilbert Spaces

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DOI: https://doi.org/10.28924/2291-8639-23-2025-160
Published: Jun 26, 2025
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L. Mokaba, Hammed A. Abass, Olawale K. Oyewole, Koketso P. Malebana, Accelerated Self-Adaptive Method for Solving Nonsmooth Convex Minimization Problem in Real Hilbert Spaces, Int. J. Anal. Appl., 23 (2025), 160.

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L. Mokaba, Hammed A. Abass, Olawale K. Oyewole, Koketso P. Malebana

Abstract

In this manuscript, we propose a proximal gradient type algorithm together with a two step inertia method for approximating solution of convex minimization problem in real Hilbert spaces. The proposed proximal gradient type method is designed in such a way that it does not depend on the Lipschitz constant. Using a self-adaptive rule, we obtain a weak convergence result under the condition that the gradient function of one of the convex functions is uniformly continuous. Preliminary numerical results show that our proposed method has a better convergence in comparison to some other related results in the literature.

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