期刊
SIAM JOURNAL ON OPTIMIZATION
卷 14, 期 3, 页码 773-782出版社
SIAM PUBLICATIONS
DOI: 10.1137/S1052623403427859
关键词
Hilbert space; maximal monotone operator; proximal point; inexact iteration; relative error; separating hyperplane; orthogonal projection; relaxation; weak convergence
This paper introduces a general implicit iterative method for finding zeros of a maximal monotone operator in a Hilbert space which unifies three previously studied strategies: relaxation, inertial type extrapolation and projection step. The first two strategies are intended to speed up the convergence of the standard proximal point algorithm, while the third permits one to perform inexact proximal iterations with fixed relative error tolerance. The paper establishes the global convergence of the method for the weak topology under appropriate assumptions on the algorithm parameters.
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