Computer Science

Computer Science ›› 2024, Vol. 51 ›› Issue (5): 232-241.doi: 10.11896/jsjkx.240200027

• Artificial Intelligence • Previous Articles     Next Articles

Linear Inertial ADMM for Nonseparable Nonconvex and Nonsmooth Problems

LIU Yang1, LIU Kang2, WANG Yongquan1   

  1. 1 Department of Intelligent Science and Information Law,East China University of Political Science and Law,Shanghai 201620,China
    2 Business school,University of Shanghai for Science and Technology,Shanghai 200093,China
  • Received:2024-02-04 Revised:2024-03-20 Online:2024-05-15 Published:2024-05-08
  • About author:LIU Yang,born in 1983,Ph.D,lectu-rer.Her main research interests include algorithm optimization and artificial intelligence.
  • Supported by:
    National Key Research and Development Program of China(2023YFC3306100,2023YFC3306105,2023YFC3306103),Major Projects of National Social Science Foundation(20&ZD199),Shanghai Philosophy and Social Science Planning Project(2023EFX011),Ministry of Education Youth Fund for Humanities and Social Sciences(20YJC820030) and Chinese Criminology Society Major Project(FZXXH2022A02).

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Abstract: In this paper,a linear inertial alternating direction multiplier method (LIADMM ) is proposed for the nonconvex non-smooth miniaturisation problem of the objective function containing the coupling function H(x,y),and to facilitate the solution of the subproblems,the objective function is linearised and the inertial effect is introduced into the x-subproblem.To facilitate the solution of the subproblem,the coupling function H(x,y) is linearised in the objective function and the inertial effect is introduced into the x-subproblem.The global convergence of the algorithm is established under appropriate assumptions,and the strong convergence of the algorithm is proved by introducing auxiliary functions satisfying the Kurdyka-Łojasiewicz inequality.Two numerical experiments show that the algorithm with the introduction of inertial effect converges has better convergence performance than the algorithm without inertial effect.

Key words: Coupling function H(x, y), Nonconvex nonsmooth optimization, Alternating direction method of multipliers (ADMM), Inertial effect, Kurdyka-Łojasiewicz inequality

CLC Number: 

  • TP301.6
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