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Strong convergence results for convex minimization and monotone variational inclusion problems in Hilbert space

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Abstract

In this paper, we propose a new modification of the Gradient Projection Algorithm and the Forward–Backward Algorithm. Using our proposed algorithms, we establish two strong convergence theorems for solving convex minimization problem, monotone variational inclusion problem and fixed point problem for demicontractive mappings in a real Hilbert space. Furthermore, we apply our results to solve split feasibility and optimal control problems. We also give two numerical examples of our algorithm in real Euclidean space of dimension 4 and in an infinite dimensional Hilbert space, to show the efficiency and advantage of our results.

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Acknowledgements

The first author acknowledge with thanks the bursary and financial support from Department of Science and Technology and National Research Foundation, Republic of South Africa Center of Excellence in Mathematical and Statistical Sciences (DST-NRF COE-MaSS) Doctoral Bursary. Opinions expressed and conclusions arrived are those of the authors and are not necessarily to be attributed to the CoE-MaSS. The authors would like to thank the anonymous referees for carefully reading the paper and providing useful and interesting comments that have greatly improved the paper.

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Authors and Affiliations

  1. School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa

    C. C. Okeke, C. Izuchukwu & O. T. Mewomo

  2. DST-NRF Center of Excellence in Mathematical and Statistical Sciences (CoE-MaSS), Johannesburg, South Africa

    C. C. Okeke

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  1. C. C. Okeke
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  2. C. Izuchukwu
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  3. O. T. Mewomo
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Correspondence to O. T. Mewomo.

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Okeke, C.C., Izuchukwu, C. & Mewomo, O.T. Strong convergence results for convex minimization and monotone variational inclusion problems in Hilbert space. Rend. Circ. Mat. Palermo, II. Ser 69, 675–693 (2020). https://doi.org/10.1007/s12215-019-00427-y

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