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

Maryam Yashtini ()
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Maryam Yashtini: Georgetown University

Journal of Global Optimization, 2022, vol. 84, issue 4, No 4, 913-939

Abstract: 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.

Keywords: Nonconvex and nonsmooth optimization; Kurdyka-Łojasiewicz inequality; Alternating direction method of multiplier (ADMM); Convergence; convergence rate; Variable metric proximal terms (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10898-022-01174-8

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