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A New Gradient Projection Algorithm for Convex Minimization Problem and its Application to Split Feasibility Problem

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Abstract

In this paper, we study convergence analysis of a new gradient projection algorithm for solving convex minimization problems in Hilbert spaces. We observe that the proposed gradient projection algorithm weakly converges to a minimum of convex function f which is defined from a closed and convex subset of a Hilbert space to \(\mathbb {R}\). Also, we give a nontrivial example to illustrate our result in an infinite dimensional Hilbert space. We apply our result to solve the split feasibility problem.

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Acknowledgements

The authors is very grateful to the referees for their valuable comments and suggestions.

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  1. Department of Mathematics, Adiyaman University, Adiyaman, Turkey

    Müzeyyen Ertürk & Asiye Kızmaz

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  1. Müzeyyen Ertürk
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  2. Asiye Kızmaz
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Correspondence to Müzeyyen Ertürk.

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Ertürk, M., Kızmaz, A. A New Gradient Projection Algorithm for Convex Minimization Problem and its Application to Split Feasibility Problem. Vietnam J. Math. 50, 29–44 (2022). https://doi.org/10.1007/s10013-020-00463-7

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  • DOI: https://doi.org/10.1007/s10013-020-00463-7

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