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An extension of the auxiliary problem principle to nonsymmetric auxiliary operators. (English) Zbl 0918.47044
From the abstract: “To find a zero of a maximal monotone operator, an extension of the auxiliary problem principle to nonsymmetric auxiliary operators is proposed. The main convergence result supposes a relationship between the operator and the nonsymmetric component of the auxiliary operator. When applied to the particular case of convex-concave functions, this result implies the convergence of the parallel version of the Arrow-Hurwicz algorithm under the assumptions of Lipschitz and partial Dunn properties of the main operator. The latter is systematically enforced by partial regularization. In the strongly monotone case, it is shown that the convergence is linear in the average. Moreover, if the symmetric part of the auxiliary operator is linear, then the Lipschitz property of the universe suffices to ensure a linear convergence rate in the average”.

MSC:
47H05 Monotone operators and generalizations
65J15 Numerical solutions to equations with nonlinear operators (do not use 65Hxx)
47J25 Iterative procedures involving nonlinear operators
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