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A proximal point algorithm for zeros of monotone operators

A proximal point algorithm for zeros of monotone operators

... Huang, Strong convergence theorems for fixed point problems and generalized equilibrium problems of three relatively quasi-nonexpansive mappings in Banach spaces, J.. Zhou, Approximate p[r] ... See full document

7

A modified regularization method for finding zeros of monotone operators in Hilbert spaces

A modified regularization method for finding zeros of monotone operators in Hilbert spaces

... algorithm [, ]. If A ≡ , then we obtain the proximal point algorithm [–] and if B ≡ , then we obtain the gradient method []. However, it is noted that the sequences generated by these ... See full document

10

Weak convergence theorems for split feasibility problems on zeros of the sum of monotone operators and fixed point sets in Hilbert spaces

Weak convergence theorems for split feasibility problems on zeros of the sum of monotone operators and fixed point sets in Hilbert spaces

... ments in the solution set of the problem (.) are called the zeros of maximal monotone operator. This problem was introduced by Martinet [], and later it has been studied by many authors. It is well known ... See full document

17

Iterative Approaches to Find Zeros of Maximal Monotone Operators by Hybrid Approximate Proximal Point Methods

Iterative Approaches to Find Zeros of Maximal Monotone Operators by Hybrid Approximate Proximal Point Methods

... inexact proximal point method ...approximate proximal point algorithms in Hilbert spaces; that is, they established strong and weak convergence theorems for modified approximate ... See full document

18

A new iteration process for equilibrium, variational inequality, fixed point problems, and zeros of maximal monotone operators in a Banach space

A new iteration process for equilibrium, variational inequality, fixed point problems, and zeros of maximal monotone operators in a Banach space

... fixed point set, the solutions of equilibrium problems, the solution set of variational inequality problems, and the set of zeros of maximal monotone operators in a uniformly smooth and ... See full document

18

Convergence of a proximal point algorithm for maximal monotone operators in Hilbert spaces

Convergence of a proximal point algorithm for maximal monotone operators in Hilbert spaces

... maximal monotone operators has emerged as an effective and powerful tool for studying many real world problems arising in various branches of social, physi- cal, engineering, pure and applied sciences in ... See full document

10

An Extragradient Method and Proximal Point Algorithm for Inverse Strongly Monotone Operators and Maximal Monotone Operators in Banach Spaces

An Extragradient Method and Proximal Point Algorithm for Inverse Strongly Monotone Operators and Maximal Monotone Operators in Banach Spaces

... maximal monotone operator and the solution set of the variational inequality problem for an inverse-strongly-monotone operator in a 2-uniformly convex and uniformly smooth Banach ...zero point of a ... See full document

16

Hybrid Proximal Point Methods for Zeros of Maximal Monotone Operators, Variational Inequalities and Mixed Equilibrium Problems

Hybrid Proximal Point Methods for Zeros of Maximal Monotone Operators, Variational Inequalities and Mixed Equilibrium Problems

... The set of solutions of the variational inequality problem is denoted by VIC, A. Such a problem is connected with the convex minimization problem, the complementarity problem, the problem of finding a point u ∈ E ... See full document

32

Strong convergence theorems for a class of split feasibility problems and fixed point problem in Hilbert spaces

Strong convergence theorems for a class of split feasibility problems and fixed point problem in Hilbert spaces

... ments in the solution set of problem (1.2) are called the zeros of this maximal monotone operator. This problem was introduced by Martinet [4], and later it has been studied by many authors. It is well ... See full document

15

Approximation of zeros of bounded maximal monotone mappings, solutions of Hammerstein integral equations and convex minimization problems

Approximation of zeros of bounded maximal monotone mappings, solutions of Hammerstein integral equations and convex minimization problems

... J-fixed point of T ...maximal monotone maps is obtained, which is also a complement of the proximal point algorithm of Martinet [] and Rockafellar [], which has also been studied by ... See full document

28

Some results on an infinite family of accretive operators in a reflexive Banach space

Some results on an infinite family of accretive operators in a reflexive Banach space

... In this article, we investigate common zeros of an infinite family of accretive operators based on a Halpern-like proximal point algorithm. Strong convergence theorems are es- tablished ... See full document

11

A general inexact iterative method for monotone operators, equilibrium problems and fıxed point problems of semigroups in Hilbert spaces

A general inexact iterative method for monotone operators, equilibrium problems and fıxed point problems of semigroups in Hilbert spaces

... fixed point x ∗ ∈ F(T ) , where F(T ) denotes the set of common fixed point of the nonexpansive ...The point x * solves the variational in-equality 〈(g f −A ) x* , x−x*〉 ≤ 0 for all x ∈ F(T ) ...to ... See full document

19

Regularization Inertial Proximal Point Algorithm for Monotone Hemicontinuous Mapping and Inverse Strongly Monotone Mappings in Hilbert Spaces

Regularization Inertial Proximal Point Algorithm for Monotone Hemicontinuous Mapping and Inverse Strongly Monotone Mappings in Hilbert Spaces

... inertial proximal algorithm was proposed by Alvarez 7 in the context of convex ...maximal monotone operators. Recently, Moudafi 9 applied this algorithm for variational inequalities; ... See full document

10

Inertial proximal algorithm for difference of two maximal monotone operators

Inertial proximal algorithm for difference of two maximal monotone operators

... the zeros of difference of two maximal monotone ...an algorithm for difference of two maximal monotone operators plays a central role in the study of DC programming [8, ...two ... See full document

8

Common Zero Points of Two Finite Families of Maximal Monotone Operators via Proximal Point Algorithms

Common Zero Points of Two Finite Families of Maximal Monotone Operators via Proximal Point Algorithms

... A point p in closed and convex subset C of E is called an asymptotic fixed point of T [14] if C contains a sequence {x n } which converges weakly to p such that lim n→∞ kx n − T x n k = ... See full document

27

Composite iterative schemes for maximal monotone operators in reflexive Banach spaces

Composite iterative schemes for maximal monotone operators in reflexive Banach spaces

... the proximal point algorithms for finding a com- mon element in the set N i=1 A − i 1 (0 ∗ ...our algorithm is different from that of Reich and Sabach [11] which is based on a finite intersection of ... See full document

10

Extragradient subgradient methods for solving bilevel equilibrium problems

Extragradient subgradient methods for solving bilevel equilibrium problems

... simple proximal method and proved the weak convergence to a solution of problem ...the algorithm by combining the proximal method with the Halpern method for solving bilevel monotone ... See full document

21

Convergence analysis of an iterative algorithm for monotone operators

Convergence analysis of an iterative algorithm for monotone operators

... nonlinear operators. Study of fixed (zero) point approximation algorithms for computing fixed (zero) points constitutes now a topic of in- tensive research ...a point in the intersection of these ... See full document

14

An algorithm for treating asymptotically strict pseudocontractions and monotone operators

An algorithm for treating asymptotically strict pseudocontractions and monotone operators

... The motivation for the common element problem is mainly due to its possible appli- cations to mathematical modeling of concrete complex problems. The common element problems include mini-max problems, complementarity ... See full document

14

Strong convergence of a splitting algorithm for treating monotone operators

Strong convergence of a splitting algorithm for treating monotone operators

... or of the same difficult as the original zero point problem. Therefore, one of the most inter- esting and important problems in the theory of monotone operators is to find an efficient iterative ... See full document

15

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