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Adaptive Douglas–Rachford Algorithms for Biconvex Optimization Problem in the Finite Dimensional Real Hilbert Spaces

Author

Listed:
  • Ming-Shr Lin

    (Department of Risk Management and Insurance, Feng Chia University, Taichung 407102, Taiwan)

  • Chih-Sheng Chuang

    (Department of Applied Mathematics, National Chiayi University, Chiayi 600355, Taiwan)

Abstract

In this paper, we delve into the realm of biconvex optimization problems, introducing an adaptive Douglas–Rachford algorithm and presenting related convergence theorems in the setting of finite-dimensional real Hilbert spaces. It is worth noting that our approach to proving the convergence theorem differs significantly from those in the literature.

Suggested Citation

  • Ming-Shr Lin & Chih-Sheng Chuang, 2024. "Adaptive Douglas–Rachford Algorithms for Biconvex Optimization Problem in the Finite Dimensional Real Hilbert Spaces," Mathematics, MDPI, vol. 12(23), pages 1-15, November.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:23:p:3785-:d:1533453
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    References listed on IDEAS

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    1. Francisco J. Aragón Artacho & Rubén Campoy, 2018. "A new projection method for finding the closest point in the intersection of convex sets," Computational Optimization and Applications, Springer, vol. 69(1), pages 99-132, January.
    2. Francisco Aragón Artacho & Jonathan Borwein, 2013. "Global convergence of a non-convex Douglas–Rachford iteration," Journal of Global Optimization, Springer, vol. 57(3), pages 753-769, November.
    3. Jochen Gorski & Frank Pfeuffer & Kathrin Klamroth, 2007. "Biconvex sets and optimization with biconvex functions: a survey and extensions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 66(3), pages 373-407, December.
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