Acta mathematica scientia,Series A ›› 2023, Vol. 43 ›› Issue (1): 291-304.

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Convergence Analysis of Bregman ADMM for Three-Block Nonconvex Indivisible Optimization Problems with Linearization Technique

Fuqin Liu,Jianwen Peng*(),Honglin Luo   

  1. School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331
  • Received:2022-03-31 Revised:2022-08-05 Online:2023-02-26 Published:2023-03-07
  • Supported by:
    The NSFC(11991024);The NSFC(12271071);Team Project of Innovation Leading Talent in Chongqing(CQYC20210309536);Contract System Project of Chongqing Talent Plan(cstc2022ycjh-bgzxm0147);Chongqing University Innovation Research Group Project(CXQT20014);Chongqing Natural Science Foundation Project(cstc2021jcyj-msxmX0300)


Alternating direction multiplier method is an effective method to solve two separable convex optimization problems, but the convergence of alternating direction multiplier method may not be guaranteed for three nonseparable nonconvex optimization problems. This paper mainly studies the convergence analysis of the linearized generalized Bregman alternating direction multiplier method (L-G-BADMM) for solving the nonconvex minimization problem whose objective function is three indivisible blocks. Under appropriate assumptions, we solve the subproblem of the algorithm and construct a benefit function satisfying Kurdyka-Lojasiewicz property. The convergence of the algorithm can be obtained through theoretical proof.

Key words: Bregman divergence, ADMM, Kurdyka-Lojasiewicz property, Linearization

CLC Number: 

  • O221.2