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Rockafellar’s celebrated theorem based on \(A\)-maximal monotonicity design. (English) Zbl 1148.47039

The author extends a well-known result on the proximal point method for finding zeroes of maximal monotone operators [cf.R.T.Rockafellar, SIAM J. Control Optimization 14, 877–898 (1976; Zbl 0358.90053)] to the general framework for \(A\)-maximal monotonicity (also referred to as the \(A\)-monotonicity framework in literature). The latter concept generalizes the theory of set-valued maximal monotone mappings, including the notion of \(H\)-maximal monotonicity (also referred to as \(H\)-monotonicity).

MSC:

47H05 Monotone operators and generalizations
47J25 Iterative procedures involving nonlinear operators
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.

Citations:

Zbl 0358.90053
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References:

[1] Rockafellar, R. T., Monotone operators and the proximal point algorithm, SIAM J. Control Optim., 14, 877-898 (1976) · Zbl 0358.90053
[2] Rockafellar, R. T., Augmented Lagrangians and applications of the proximal point algorithm in convex programming, Math. Oper. Res., 1, 97-116 (1976) · Zbl 0402.90076
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[7] Eckstein, J.; Bertsekas, D., On the Douglas-Rachford splitting and the proximal point algorithm for maximal monotone operators, Math. Program., 55, 293-318 (1992) · Zbl 0765.90073
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