Under weak smoothness of f and prox-regularity of g, the high-order forward-backward envelope is differentiable and its gradient is Hölder continuous near p-calm points of the composite objective.
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On fundamental properties of high-order forward-backward envelope
Under weak smoothness of f and prox-regularity of g, the high-order forward-backward envelope is differentiable and its gradient is Hölder continuous near p-calm points of the composite objective.