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We propose generic acceleration schemes for a wide class of optimization and iterative schemes based on relaxation and inertia. In particular, we introduce methods that automatically tune the acceleration coefficients online and establish their convergence. This is made possible by considering classes of fixed-point iterations over averaged operators which encompass gradient methods, ADMM (Alternating Direction Method of Multipliers), primal dual algorithms and so on.
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Iutzeler et al. (2017) studied this question.
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