An Approximate Proximal Point Algorithm for Maximal Monotone Inclusion Problems
نویسندگان
چکیده
منابع مشابه
An Approximate Proximal Point Algorithm for Maximal Monotone Inclusion Problems
This paper presents and analyzes a strongly convergent approximate proximal point algorithm for finding zeros of maximal monotone operators in Hilbert spaces. The proposed method combines the proximal subproblem with a more general correction step which takes advantage of more information on the existing iterations. As applications, convex programming problems and generalized variational inequa...
متن کاملConvergence 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 کاملA Proximal Point Algorithm for Finding a Common Zero of a Finite Family of Maximal Monotone Operators
In this paper, we consider a proximal point algorithm for finding a common zero of a finite family of maximal monotone operators in real Hilbert spaces. Also, we give a necessary and sufficient condition for the common zero set of finite operators to be nonempty, and by showing that in this case, this iterative sequence converges strongly to the metric projection of some point onto the set of c...
متن کاملA Hybrid Approximate Extragradient – Proximal Point Algorithm Using the Enlargement of a Maximal Monotone Operator
We propose a modification of the classical extragradient and proximal point algorithms for finding a zero of a maximal monotone operator in a Hilbert space. At each iteration of the method, an approximate extragradient-type step is performed using information obtained from an approximate solution of a proximal point subproblem. The algorithm is of a hybrid type, as it combines steps of the extr...
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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematical Problems in Engineering
سال: 2011
ISSN: 1024-123X,1563-5147
DOI: 10.1155/2011/262073