Proximal Minimization Algorithm with D-Functions 1'2

The original proximal minimization algorithm employs quadratic additive terms in the objectives of the subproblems. In this paper, we replace these quadratic additive terms by more general D- functions which resemble (but are not strictly) distance functions. We characterize the properties of such D-functions which, when used in the proximal minimization algorithm, preserve its overall convergence. The quadratic case as well as an entropy-oriented proximal minimization algorithm are obtained as special cases.

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