Convergence analysis for proximal gradient-type methods with arbitrary proximal terms in nonconvex composite optimization, without requiring the global descent property between the smooth function and its proximal mapping.
A descent lemma beyond lipschitz gradient continuity: first-order methods revisited and applications.Mathematics of Operations Research, 42(2): 330–348
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Proximal gradient-type method with generalized distance and convergence analysis without global descent lemma
Convergence analysis for proximal gradient-type methods with arbitrary proximal terms in nonconvex composite optimization, without requiring the global descent property between the smooth function and its proximal mapping.