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标题:Global Convergence of ADMM in Nonconvex Nonsmooth Optimization
时间:2019-08-14 16:40:30
DOI:10.1007/s10915-018-0757-z
作者:Yu Wang;Wotao Yin;Jinshan Zeng
出版源: 《Journal of Scientific Computing》 ,2018 ,78 (1) :1-35
摘要:Global Convergence of ADMM in Nonconvex Nonsmooth OptimizationMathematics - Optimization and ControlComputer Science - Numerical AnalysisMathematics - Numerical AnalysisIn this paper, we analyze the convergence of the alternating direction method of multipliers (ADMM) for minimizing a nonconvex and possibly nonsmooth objective function, [equation], subject to......
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页数:36 PAGES
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目录:
  • Global Convergence of ADMM in Nonconvex Nonsmooth Optimization
    • Abstract
    • 1 Introduction
      • 1.1 Proposed Algorithm
      • 1.2 Relation to the Augmented Lagrangian Method (ALM)
      • 1.3 Related Literature
      • 1.4 Contribution and Novelty
      • 1.5 Notation and Organization
    • 2 Main Results
      • 2.1 Definitions
      • 2.2 Main Theorems
    • 3 Proof
      • 3.1 Keystones
      • 3.2 Preliminaries
      • 3.3 Main Proof
    • 4 Discussion
      • 4.1 Tightness of Assumptions
      • 4.2 Primal Variables' Update Order in ADMM
      • 4.3 Inexact Optimization of Subproblems
    • 5 Applications
      • (A) Statistical Learning
      • (B) Minimization on Compact Manifolds
      • (C) Smooth Optimization Over Complementarity Constraints
      • (D) Matrix Decomposition
    • 6 Conclusion
    • Acknowledgements
    • Appendix
    • References

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