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Subgradient projection methods extended to monotone bilevel equilibrium problems in Hilbert spaces

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Abstract

In this paper, by basing on the inexact subgradient and projection methods presented by Santos et al. (Comput. Appl. Math. 30: 91–107, 2011), we develop subgradient projection methods for solving strongly monotone equilibrium problems with pseudomonotone equilibrium constraints. The problem usually is called monotone bilevel equilibrium problems. We show that this problem can be solved by a simple and explicit subgradient method. The strong convergence for the proposed algorithms to the solution is guaranteed under certain assumptions in a real Hilbert space. Numerical illustrations are given to demonstrate the performances of the algorithms.

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Funding

This research is funded by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant Number 101.02-2019.303.

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Authors and Affiliations

  1. Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Pham Ngoc Anh

  2. Department of Mathematics, Hai Phong University, Haiphong, Vietnam

    Ho Phi Tu

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  1. Pham Ngoc Anh
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  2. Ho Phi Tu
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Correspondence to Pham Ngoc Anh.

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Anh, P.N., Tu, H.P. Subgradient projection methods extended to monotone bilevel equilibrium problems in Hilbert spaces. Numer Algor 86, 55–74 (2021). https://doi.org/10.1007/s11075-020-00878-w

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  • DOI: https://doi.org/10.1007/s11075-020-00878-w

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