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Multiblock ADMM for nonsmooth nonconvex optimization with nonlinear coupling constraints

arXiv 2201.07657 ↗First posted 19 Jan 2022math.OC cs.LGcited by 0

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Abstract (arXiv)

This paper proposes a multiblock alternating direction method of multipliers for solving a class of multiblock nonsmooth nonconvex optimization problem with nonlinear coupling constraints. We employ a majorization minimization procedure in the update of each block of the primal variables. Subsequential and global convergence of the generated sequence to a critical point of the augmented Lagrangian are proved. We also establish iteration complexity and provide preliminary numerical results for the proposed algorithm.

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References · 19

  1. 2016Least Squares Generative Adversarial Networkscited by 1,000
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  11. 2017Linearized ADMM for Non-convex Non-smooth Optimization with Convergence Analysiscited by 12
  12. 2016Unifying abstract inexact convergence theorems and block coordinate variable metric iPianocited by 10
7 more
  1. 2016Efficient Algorithms for Large-scale Generalized Eigenvector Computation and Canonical Correlation Analysiscited by 10
  2. 2018Nonconvex Lagrangian-Based Optimization: Monitoring Schemes and Global Convergencecited by 7
  3. 2017Iteration-complexity of a Jacobi-type non-Euclidean ADMM for multi-block linearly constrained nonconvex programscited by 5
  4. 2021Block Alternating Bregman Majorization Minimization with Extrapolationcited by 4
  5. 2014A Block Successive Upper Bound Minimization Method of Multipliers for Linearly Constrained Convex Optimizationcited by 3
  6. 2020Extrapolated Proximal Subgradient Algorithms for Nonconvex and Nonsmooth Fractional Programscited by 3
  7. 2021A Framework of Inertial Alternating Direction Method of Multipliers for Non-Convex Non-Smooth Optimizationcited by 3

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