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Alternating direction method of multipliers for linear hyperspectral unmixing

Author

Listed:
  • Yu-Hong Dai

    (Chinese Academy of Sciences)

  • Fangfang Xu

    (Shandong University of Science and Technology)

  • Liwei Zhang

    (Dalian University of Technology)

Abstract

Linear hyperspectral unmixing (LHU) is a class of important problems in remote sensing. It can be modelled by a linearly constrained convex optimization problem with a coupled objective function. This paper proposes an alternating direction method of multipliers (ADMM) for solving this LHU model. The special structure of the LHU model allows explicit solutions to the subproblems in the ADMM and hence the ADMM is easily implementable. The global convergence of the ADMM is established despite the existence of a coupled term in the objective function. Our numerical experiments with four data sets demonstrated that the proposed ADMM is effective for solving the LHU model.

Suggested Citation

  • Yu-Hong Dai & Fangfang Xu & Liwei Zhang, 2023. "Alternating direction method of multipliers for linear hyperspectral unmixing," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 97(3), pages 289-310, June.
    • Handle: RePEc:spr:mathme:v:97:y:2023:i:3:d:10.1007_s00186-023-00815-2
    DOI: 10.1007/s00186-023-00815-2
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    References listed on IDEAS

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    1. Ying Cui & Xudong Li & Defeng Sun & Kim-Chuan Toh, 2016. "On the Convergence Properties of a Majorized Alternating Direction Method of Multipliers for Linearly Constrained Convex Optimization Problems with Coupled Objective Functions," Journal of Optimization Theory and Applications, Springer, vol. 169(3), pages 1013-1041, June.
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