We propose a multi-step inertial Forward-Backward splitting algorithm for minimizing the sum of two non-necessarily convex functions, one of which is proper lower semi-continuous while the other is differentiable with a Lipschitz continuous gradient. We first prove global convergence of the algorithm with the help of the Kurdyka-Łojasiewicz property. Then, when the non-smooth part is also partly smooth relative to a smooth submanifold, we establish finite identification of the latter and provide sharp local linear convergence analysis. The proposed method is illustrated on several problems arising from statistics and machine learning.

Let M denote M = 2 1 1 2 1 . . . . . . . . . 1 2 1 1 2 R

The conditions on the representation that imply global convergence are different between these two algorithms.

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These shifts are defined via parametric changes in the causal mechanisms of observed variables, where constraints on parameters yield a "robustness set" of plausible distributions and acorresponding worst-case loss overthe set.