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A Greedy Newton-Type Method for Multiple Sparse Constraint Problem

Author

Listed:
  • Jun Sun

    (Linyi University)

  • Lingchen Kong

    (Beijing Jiaotong University)

  • Biao Qu

    (Qufu Normal University)

Abstract

With the development of science and technology, we can get many groups of data for the same object. There is a certain relationship with each other or structure between these data or within the data. To characterize the structure of the data in different datasets, in this paper, we propose a multiple sparse constraint problem (MSCP) to process the problem with multiblock sparse structure. We give three types of stationary points and present the relationships among the three types of stationary points and the global/local minimizers. Then we design a gradient projection Newton algorithm, which is proven to enjoy the global and quadratic convergence property. Finally, some numerical experiments of different examples illustrate the efficiency of the proposed method.

Suggested Citation

  • Jun Sun & Lingchen Kong & Biao Qu, 2023. "A Greedy Newton-Type Method for Multiple Sparse Constraint Problem," Journal of Optimization Theory and Applications, Springer, vol. 196(3), pages 829-854, March.
    • Handle: RePEc:spr:joptap:v:196:y:2023:i:3:d:10.1007_s10957-022-02156-2
    DOI: 10.1007/s10957-022-02156-2
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    References listed on IDEAS

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    1. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67, February.
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