Approximating Solutions of Maximal Monotone Operators in Hilbert Spaces
نویسندگان
چکیده
منابع مشابه
Research Article Iterative Algorithm for Approximating Solutions ofMaximal Monotone Operators in Hilbert Spaces
where {rn} ⊂ (0,∞) and Jr = (I + rT)−1 for all r > 0. This algorithm was first introduced by Martinet [1]. Rockafellar [2] proved that if liminfn→∞ rn > 0 and T−10 = ∅, then the sequence {xn} defined by (1.1) converges weakly to an element of T−10. Later, many researchers have studied the convergence of the sequence defined by (1.1) in a Hilbert space; see, for instance, [3–6] and the reference...
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15 صفحه اولConvergence Theorems of Approximate Proximal Point Algorithm for Zeroes of Maximal Monotone Operators in Hilbert Spaces
In this paper, we introduce two kinds of iterative algorithms for finding zeroes of maximal monotone operators, and establish strong and weak convergence theorems of the modified proximal point algorithms. By virtue of the established theorems, we consider the problem of finding a minimizer of a convex function. Mathematics Subject Classification: Primary 47H17; Secondary 47H05, 47H10
متن کاملConvergence of a proximal point algorithm for maximal monotone operators in Hilbert spaces
* Correspondence: hbshigh@yeah. net College of Science, Hebei University of Engineering, Handan 056038, China Full list of author information is available at the end of the article Abstract In this article, we consider the proximal point algorithm for the problem of approximating zeros of maximal monotone mappings. Strong convergence theorems for zero points of maximal monotone mappings are est...
متن کاملApproximate Proximal Point Algorithms for Finding Zeroes of Maximal Monotone Operators in Hilbert Spaces
LetH be a real Hilbert space, Ω a nonempty closed convex subset ofH, and T : Ω → 2 a maximal monotone operator with T−10/ ∅. Let PΩ be the metric projection of H onto Ω. Suppose that, for any given xn ∈ H, βn > 0, and en ∈ H, there exists xn ∈ Ω satisfying the following set-valued mapping equation: xn en ∈ xn βnT xn for all n ≥ 0, where {βn} ⊂ 0, ∞ with βn → ∞ as n → ∞ and {en} is regarded as a...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 2000
ISSN: 0021-9045
DOI: 10.1006/jath.2000.3493