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Proximal minimization algorithm with \(D\)-functions. (English) Zbl 0794.90058
Summary: The original proximal minimization algorithm employs quadratic additive terms in the objective of the subproblems. 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.

90C30 Nonlinear programming
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