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A parallel combination extragradient method with Armijo line searching for finding common solutions of finite families of equilibrium and fixed point problems

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Abstract

In this paper, we introduce a new parallel combination extragradient method for solving a finite family of pseudo-monotone equilibrium problems and finding a common fixed point of a finite family of demicontractive mappings in Hilbert space. The algorithm is designed such that at each iteration a single strongly convex program is solved and the stepsize is determined via an Armijo line searching technique. Also, the algorithm make a single projection onto a sub-level set which is constructed by the convex combination of finite convex functions. Under certain mild-conditions, we state and prove a strong convergence theorem for approximating a common solution of a finite family of equilibrium problems with pseudo-monotone bifunctions and a finite family of demicontractive mappings. Finally, we present numerical examples to illustrate the applicability of the algorithm proposed. This method improves many of the existing methods in the literature.

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Acknowledgements

The authors thank the anonymous referees for valuable and useful suggestions and comments which led to the great improvement of the paper.

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

    L. O. Jolaoso, T. O. Alakoya, A. Taiwo & O. T. Mewomo

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  1. L. O. Jolaoso
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  2. T. O. Alakoya
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  3. A. Taiwo
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  4. O. T. Mewomo
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Correspondence to O. T. Mewomo.

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Jolaoso, L.O., Alakoya, T.O., Taiwo, A. et al. A parallel combination extragradient method with Armijo line searching for finding common solutions of finite families of equilibrium and fixed point problems. Rend. Circ. Mat. Palermo, II. Ser 69, 711–735 (2020). https://doi.org/10.1007/s12215-019-00431-2

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