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Convergence and rate analysis of a proximal linearized ADMM for nonconvex nonsmooth optimization

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  • Maryam Yashtini

    (Georgetown University)

Abstract

In this paper, we consider a proximal linearized alternating direction method of multipliers, or PL-ADMM, for solving linearly constrained nonconvex and possibly nonsmooth optimization problems. The algorithm is generalized by using variable metric proximal terms in the primal updates and an over-relaxation step in the multiplier update. Extended results based on the augmented Lagrangian including subgradient band, limiting continuity, descent and monotonicity properties are established. We prove that the PL-ADMM sequence is bounded. Under the powerful Kurdyka-Łojasiewicz inequality we show that the PL-ADMM sequence has a finite length thus converges, and we drive its convergence rates.

Suggested Citation

  • Maryam Yashtini, 2022. "Convergence and rate analysis of a proximal linearized ADMM for nonconvex nonsmooth optimization," Journal of Global Optimization, Springer, vol. 84(4), pages 913-939, December.
    • Handle: RePEc:spr:jglopt:v:84:y:2022:i:4:d:10.1007_s10898-022-01174-8
    DOI: 10.1007/s10898-022-01174-8
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    References listed on IDEAS

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