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Proximal Subgradient Algorithm for a Class of Nonconvex Bilevel Equilibrium Problems

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Abstract

In this paper, we propose an algorithm for a bilevel problem of solving a monotone equilibrium problem over the solution set of a mixed equilibrium problem involving prox-convex functions in finite dimensional Euclidean space \(\mathbb R^n\). The proposed algorithm is based on the proximal method for mixed variational inequalities by using proximal operators of prox-convex functions. The convergence of the sequences generated by the proposed algorithm is established. Furthermore, some consequences of the main result are given. Finally, we provide numerical examples to illustrate our algorithm;s convergence and compare it with others. As an application, we apply the proposed algorithm to solve a modified oligopolistic Nash–Cournot equilibrium model.

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Acknowledgements

The author would like to thank the Editor and the referees for their comments on the manuscript which helped in improving the earlier version of this paper.

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  1. Faculty of Natural Sciences, Electric Power University, Hanoi, Vietnam

    Tran Van Thang

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  1. Tran Van Thang
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Correspondence to Tran Van Thang.

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Thang, T.V. Proximal Subgradient Algorithm for a Class of Nonconvex Bilevel Equilibrium Problems. Bull. Malays. Math. Sci. Soc. 47, 65 (2024). https://doi.org/10.1007/s40840-024-01664-w

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