# Generalized relaxation of string averaging operators based on strictly relaxed cutter operators

@inproceedings{Nikazad2017GeneralizedRO, title={Generalized relaxation of string averaging operators based on strictly relaxed cutter operators}, author={Touraj Nikazad and Mahdi Mirzapour}, year={2017} }

Abstract. We present convergence analysis of a generalized relaxation of string averaging operators which is based on strictly relaxed cutter operators on a general Hilbert space. In this paper, the string averaging operator is assembled by averaging of strings’ endpoints and each string consists of composition of finitely many strictly relaxed cutter operators. We also consider projected version of the generalized relaxation of string averaging operator. To evaluate the study, we recall a wide…

#### 3 Citations

A string averaging method based on strictly quasi-nonexpansive operators with generalized relaxation

- Computer Science, MathematicsArXiv
- 2021

A fixed point iterative method based on generalized relaxation of strictly quasi-nonexpansive operators for solving linear systems of equations (inequalities) and the subgradient projection method for solving nonlinear convex feasibility problems is studied.

Linear convergence rates for extrapolated fixed point algorithms

- MathematicsOptimization
- 2018

ABSTRACT We establish linear convergence rates for a certain class of extrapolated fixed point algorithms which are based on dynamic string-averaging methods in a real Hilbert space. This applies, in…

Extrapolated cyclic subgradient projection methods for the convex feasibility problems and their numerical behaviour

- MathematicsOptimization
- 2018

ABSTRACT We present two versions of the extrapolated cyclic subgradient projections method for solving the convex feasibility problem. Moreover, we present the results of numerical tests, where we…

#### References

SHOWING 1-10 OF 51 REFERENCES

On the string averaging method for sparse common fixed-point problems

- Mathematics, MedicineInt. Trans. Oper. Res.
- 2009

A definition of sparseness of a family of operators is proposed and a string-averaging algorithmic scheme is investigated that favorably handles the common fixed points problem when the family of Operators is sparse.

Convergence of String-Averaging Projection Schemes for Inconsistent Convex Feasibility Problems

- Mathematics, Computer ScienceOptim. Methods Softw.
- 2003

An algorithmic scheme is proposed which genenralizes both the string-averaging algorithm and the block-iterative projections (BIP) method with fixed blocks and proves convergence of the Stringaveraging method in the inconsistent case by translating it into a fully sequential algorithm in the product space.

Averaging Strings of Sequential Iterations for Convex Feasibility Problems

- Mathematics
- 2001

An algorithmic scheme for the solution of convex feasibility problems is proposed in which the end-points of strings of sequential projections onto the constraints are averaged. The scheme employing…

String-averaging projected subgradient methods for constrained minimization

- Computer Science, MathematicsOptim. Methods Softw.
- 2014

An algorithmic scheme is proposed that generalizes, from the algorithmic structural point of view, earlier work of Helou Neto and De Pierro, and uses the recently developed family of dynamic string-averaging projection methods wherein iteration-index-dependent variable strings and variable weights are permitted.

Convergence and perturbation resilience of dynamic string-averaging projection methods

- Mathematics, Computer ScienceComput. Optim. Appl.
- 2013

The bounded perturbation resilience of DSAP methods is relevant and important for their possible use in the framework of the recently developed superiorization heuristic methodology for constrained minimization problems.

On the Douglas—Rachford splitting method and the proximal point algorithm for maximal monotone operators

- Mathematics, Computer ScienceMath. Program.
- 1992

This paper shows, by means of an operator called asplitting operator, that the Douglas—Rachford splitting method for finding a zero of the sum of two monotone operators is a special case of the proximal point algorithm, which allows the unification and generalization of a variety of convex programming algorithms.

Stable Convergence Behavior Under Summable Perturbations of a Class of Projection Methods for Convex Feasibility and Optimization Problems

- Mathematics, Computer ScienceIEEE Journal of Selected Topics in Signal Processing
- 2007

It is proved that the algorithms in this class of projection methods converge to solutions of the consistent convex feasibility problem, and that their convergence is stable under summable perturbations.

Projection algorithms and monotone operators

- Mathematics
- 1996

This thesis consists of two parts.
In Part I, projection algorithms for solving convex feasibility problems in Hilbert space are studied. Powerful techniques from Convex Analysis are employed within…

Extrapolation and Local Acceleration of an Iterative Process for Common Fixed Point Problems

- Mathematics, Physics
- 2012

We consider sequential iterative processes for the common fixed point problem of families of cutter operators on a Hilbert space. These are operators that have the property that, for any point x\inH,…

PROPERTIES OF A CLASS OF APPROXIMATELY SHRINKING OPERATORS AND THEIR APPLICATIONS

- Mathematics
- 2014

In this paper we present an application of a class of quasi-nonexpansive operators to iterative methods for solving the following variational inequality problem VIP(F,C): Find ū ∈ C such that 〈F ū,…