Convergence rate bounds for a proximal ADMM with over-relaxation stepsize parameter for solving nonconvex linearly constrained problems

Jefferson G. Melo; Max L.N. Goncalves; Renato D.C. Monteiro

arxiv: 1702.01850 · v2 · pith:XDTCZT25new · submitted 2017-02-07 · 🧮 math.OC

Convergence rate bounds for a proximal ADMM with over-relaxation stepsize parameter for solving nonconvex linearly constrained problems

Max L.N. Goncalves , Jefferson G. Melo , Renato D.C. Monteiro This is my paper

classification 🧮 math.OC

keywords admmover-relaxationparameterproximalboundsconstrainedconvergenceinterval

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This paper establishes convergence rate bounds for a variant of the proximal alternating direction method of multipliers (ADMM) for solving nonconvex linearly constrained optimization problems. The variant of the proximal ADMM allows the inclusion of an over-relaxation stepsize parameter belonging to the interval $(0,2)$. To the best of our knowledge, all related papers in the literature only consider the case where the over-relaxation parameter lies in the interval $(0,(1+\sqrt{5})/2)$.

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