Numerical Algorithms, ISSN 1017-1398, 12/2018, Volume 79, Issue 4, pp. 1231 - 1256

In this article, we first propose an extended split equality problem which is an extension of the convex feasibility problem, and then introduce a parameter w...

Numeric Computing | Theory of Computation | Extended split equality problem | Weak convergence | Algorithms | Algebra | Numerical Analysis | Extended split equality fixed point problem | Computer Science | 47H09 | Simultaneous iterative algorithm | 47H05 | 47J25 | 47H06 | Fixed point | EIGENVALUE | MATHEMATICS, APPLIED | CONVEX FEASIBILITY | POLYNOMIAL OPTIMIZATION | HILBERT | PROJECTION METHOD | CONVERGENCE | CQ-ALGORITHM | Information science | Management science | Business schools | Equality | Methods

Numeric Computing | Theory of Computation | Extended split equality problem | Weak convergence | Algorithms | Algebra | Numerical Analysis | Extended split equality fixed point problem | Computer Science | 47H09 | Simultaneous iterative algorithm | 47H05 | 47J25 | 47H06 | Fixed point | EIGENVALUE | MATHEMATICS, APPLIED | CONVEX FEASIBILITY | POLYNOMIAL OPTIMIZATION | HILBERT | PROJECTION METHOD | CONVERGENCE | CQ-ALGORITHM | Information science | Management science | Business schools | Equality | Methods

Journal Article

Journal of Inequalities and Applications, ISSN 1029-242X, 12/2019, Volume 2019, Issue 1, pp. 1 - 13

This paper considers an iterative algorithm of solving the multiple-sets split equality problem (MSSEP) whose step size is independent of the norm of the...

Bounded Hölder regularity | Multiple-sets split equality problem | Analysis | Convergent rate | Mathematics, general | Mathematics | Applications of Mathematics | Iterative algorithms | Algorithms | Iterative methods | Regularity | Convergence

Bounded Hölder regularity | Multiple-sets split equality problem | Analysis | Convergent rate | Mathematics, general | Mathematics | Applications of Mathematics | Iterative algorithms | Algorithms | Iterative methods | Regularity | Convergence

Journal Article

Fixed Point Theory and Applications, ISSN 1687-1820, 12/2014, Volume 2014, Issue 1, pp. 1 - 8

A new convex feasibility problem, the split equality problem (SEP), has been proposed by Moudafi and Byrne. The SEP was solved through the ACQA and ARCQA...

Mathematical and Computational Biology | the minimum norm solution | Analysis | general split equality problem | Mathematics, general | Mathematics | Applications of Mathematics | Topology | Differential Geometry | strong convergence | The minimum norm solution | Strong convergence | General split equality problem | MATHEMATICS | MATHEMATICS, APPLIED | Fixed point theory | Usage | Hilbert space | Contraction operators | Feasibility | Algorithms | Convergence

Mathematical and Computational Biology | the minimum norm solution | Analysis | general split equality problem | Mathematics, general | Mathematics | Applications of Mathematics | Topology | Differential Geometry | strong convergence | The minimum norm solution | Strong convergence | General split equality problem | MATHEMATICS | MATHEMATICS, APPLIED | Fixed point theory | Usage | Hilbert space | Contraction operators | Feasibility | Algorithms | Convergence

Journal Article

Numerical Algorithms, ISSN 1017-1398, 3/2017, Volume 74, Issue 3, pp. 927 - 935

We investigate CQ algorithm for the split equality problem in Hilbert spaces. In such an algorithm, the selection of the step requires prior information on the...

CQ algorithm | Numeric Computing | Projection | Theory of Computation | Split feasibility problem | Variable-step | Algorithms | Algebra | 47J20 | Numerical Analysis | Computer Science | 47J25 | 49N45 | 65J15 | MATHEMATICS, APPLIED | FEASIBILITY PROBLEM | Equality

CQ algorithm | Numeric Computing | Projection | Theory of Computation | Split feasibility problem | Variable-step | Algorithms | Algebra | 47J20 | Numerical Analysis | Computer Science | 47J25 | 49N45 | 65J15 | MATHEMATICS, APPLIED | FEASIBILITY PROBLEM | Equality

Journal Article

Optimization, ISSN 0233-1934, 09/2015, Volume 64, Issue 9, pp. 1887 - 1906

The split equality problem has extraordinary utility and broad applicability in many areas of applied mathematics. Recently, Moudafi proposed an alternating CQ...

47H10 | split equality problem | relaxed projection algorithm | viscosity algorithm | 47H07 | projection algorithm | 47H05 | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | ALTERNATING PROXIMAL ALGORITHMS | PROJECTION METHOD | SETS | VISCOSITY APPROXIMATION METHODS | Operators | Algorithms | Matrices (mathematics) | Mathematical analysis | Norms | Projection | Estimates | Linear operators

47H10 | split equality problem | relaxed projection algorithm | viscosity algorithm | 47H07 | projection algorithm | 47H05 | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | ALTERNATING PROXIMAL ALGORITHMS | PROJECTION METHOD | SETS | VISCOSITY APPROXIMATION METHODS | Operators | Algorithms | Matrices (mathematics) | Mathematical analysis | Norms | Projection | Estimates | Linear operators

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2016, Volume 2016, Issue 1, pp. 1 - 17

The split equality problem has board applications in many areas of applied mathematics. Many researchers studied this problem and proposed various algorithms...

split feasibility problem | 49J53 | 90C25 | Analysis | split equality problem | Mathematics, general | simultaneous algorithm | Mathematics | Applications of Mathematics | 49M37 | linear inverse problem | MATHEMATICS | MATHEMATICS, APPLIED | IMAGE SUPERRESOLUTION | REGULARIZATION | Algorithms | Inverse problems | Boards | Inequalities | Paper | Nonlinearity | Feasibility | Mathematical models

split feasibility problem | 49J53 | 90C25 | Analysis | split equality problem | Mathematics, general | simultaneous algorithm | Mathematics | Applications of Mathematics | 49M37 | linear inverse problem | MATHEMATICS | MATHEMATICS, APPLIED | IMAGE SUPERRESOLUTION | REGULARIZATION | Algorithms | Inverse problems | Boards | Inequalities | Paper | Nonlinearity | Feasibility | Mathematical models

Journal Article

7.
Full Text
Relaxed two points projection method for solving the multiple-sets split equality problem

Numerical Algorithms, ISSN 1017-1398, 05/2018, Volume 78, Issue 1, pp. 263 - 275

The multiple-sets split equality problem, a generalization and extension of the split feasibility problem, has a variety of specific applications in real...

Multiple-sets split equality problem | Hilbert space | Relaxed two points projection method | Convergence | CONVEX FEASIBILITY PROBLEMS | MATHEMATICS, APPLIED | CQ-ALGORITHM | Signal processing | Business schools | Algorithms | Equality | Analysis | Methods

Multiple-sets split equality problem | Hilbert space | Relaxed two points projection method | Convergence | CONVEX FEASIBILITY PROBLEMS | MATHEMATICS, APPLIED | CQ-ALGORITHM | Signal processing | Business schools | Algorithms | Equality | Analysis | Methods

Journal Article

Optimization, ISSN 0233-1934, 12/2018, Volume 67, Issue 12, pp. 2347 - 2358

In this paper, we consider the varying stepsize gradient projection algorithm (GPA) for solving the split equality problem (SEP) in Hilbert spaces, and study...

Split equality problems | 40A05 | gradient projection algorithm | 47H10 | CQ algorithm | linear convergence | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | CONVEX FEASIBILITY | Hilbert space | Algorithms | Nonlinear programming | Regularity | Convergence

Split equality problems | 40A05 | gradient projection algorithm | 47H10 | CQ algorithm | linear convergence | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | CONVEX FEASIBILITY | Hilbert space | Algorithms | Nonlinear programming | Regularity | Convergence

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2018, Volume 2018, Issue 1, pp. 1 - 18

In this paper, we are concerned with the split equality problem (SEP) in Hilbert spaces. By converting it to a coupled fixed-point equation, we propose a new...

Split equality problem | 47J20 | Analysis | Relaxed alternating method | Mathematics, general | Mathematics | Applications of Mathematics | Split feasibility problem | 47J25 | 49N45 | 65J15 | MATHEMATICS | MATHEMATICS, APPLIED | CONVEX FEASIBILITY | PROJECTION METHOD | ITERATIVE ALGORITHMS | Computational geometry | Hilbert space | Algorithms | Convexity | Convergence | Research

Split equality problem | 47J20 | Analysis | Relaxed alternating method | Mathematics, general | Mathematics | Applications of Mathematics | Split feasibility problem | 47J25 | 49N45 | 65J15 | MATHEMATICS | MATHEMATICS, APPLIED | CONVEX FEASIBILITY | PROJECTION METHOD | ITERATIVE ALGORITHMS | Computational geometry | Hilbert space | Algorithms | Convexity | Convergence | Research

Journal Article

Optimization, ISSN 0233-1934, 09/2018, Volume 67, Issue 9, pp. 1429 - 1446

In this article, we first present a projection method with outer perturbations for the split equality problem (SEP) and establish its weak convergence. Then...

Split equality problem | relaxed projection algorithm | Halpern iteration method | projection algorithm | outer approximation method | outer perturbation | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | ALTERNATING PROXIMAL ALGORITHMS | CONVEX FEASIBILITY | ITERATIONS | STRONG-CONVERGENCE | Projection | Approximation | Convexity | Mathematical analysis | Methods

Split equality problem | relaxed projection algorithm | Halpern iteration method | projection algorithm | outer approximation method | outer perturbation | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | ALTERNATING PROXIMAL ALGORITHMS | CONVEX FEASIBILITY | ITERATIONS | STRONG-CONVERGENCE | Projection | Approximation | Convexity | Mathematical analysis | Methods

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2014, Volume 2014, Issue 1, pp. 1 - 19

Let , , be real Hilbert spaces, , be two nonempty closed convex sets, and let , be two bounded linear operators. The split equality problem (SEP) is finding ,...

Analysis | split equality problem | converge strongly | Mathematics, general | Mathematics | Applications of Mathematics | iterative algorithms | MATHEMATICS | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | APPROXIMATION | FEASIBILITY PROBLEM | THEOREMS | CQ-ALGORITHM | FIXED-POINTS | Computational geometry | Construction | Algorithms | Inequalities | Norms | Regularization | Linear operators | Convergence

Analysis | split equality problem | converge strongly | Mathematics, general | Mathematics | Applications of Mathematics | iterative algorithms | MATHEMATICS | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | APPROXIMATION | FEASIBILITY PROBLEM | THEOREMS | CQ-ALGORITHM | FIXED-POINTS | Computational geometry | Construction | Algorithms | Inequalities | Norms | Regularization | Linear operators | Convergence

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2014, Volume 2014, Issue 1, pp. 1 - 8

The multiple-sets split equality problem (MSSEP) requires finding a point , , such that , where N and M are positive integers, and are closed convex subsets of...

Analysis | split equality problem | converge strongly | Mathematics, general | Mathematics | Applications of Mathematics | iterative algorithms | MATHEMATICS | MATHEMATICS, APPLIED | FEASIBILITY PROBLEM | CQ-ALGORITHM | Computational geometry | Algorithms | Inequalities | Projection | Feasibility | Hilbert space | Mapping | Convexity

Analysis | split equality problem | converge strongly | Mathematics, general | Mathematics | Applications of Mathematics | iterative algorithms | MATHEMATICS | MATHEMATICS, APPLIED | FEASIBILITY PROBLEM | CQ-ALGORITHM | Computational geometry | Algorithms | Inequalities | Projection | Feasibility | Hilbert space | Mapping | Convexity

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2017, Volume 2017, Issue 1, pp. 1 - 11

This paper introduces a new extragradient-type method to solve the multiple-sets split equality problem (MSSEP). Under some suitable conditions, the strong...

Analysis | Mathematics, general | multiple-sets split equality problem | Mathematics | Applications of Mathematics | strong convergence | extragradient-type | VARIATIONAL-INEQUALITIES | MATHEMATICS | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | FEASIBILITY PROBLEM | MONOTONE MAPPINGS | ITERATIVE ALGORITHMS | HILBERT-SPACE | Hilbert space | Mathematical models | Algorithms | Inequalities | Convergence | Research

Analysis | Mathematics, general | multiple-sets split equality problem | Mathematics | Applications of Mathematics | strong convergence | extragradient-type | VARIATIONAL-INEQUALITIES | MATHEMATICS | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | FEASIBILITY PROBLEM | MONOTONE MAPPINGS | ITERATIVE ALGORITHMS | HILBERT-SPACE | Hilbert space | Mathematical models | Algorithms | Inequalities | Convergence | Research

Journal Article

Calcolo, ISSN 0008-0624, 12/2019, Volume 56, Issue 4, pp. 1 - 27

In this paper, using a hybrid extragradient method, we introduce a new iterative process for finding a common element of the solution set of the Split Equality...

Split equality equilibrium problem | Pseudomonotone bifunction | 47H10 | Variational inequality | Numerical Analysis | phi $$ ϕ -Lipschitz-type continuity | 47H09 | Mathematics | Theory of Computation | 47H05 | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | POINT PROBLEM | CONVEX FEASIBILITY | FEASIBILITY PROBLEM | ITERATIVE METHOD | ALGORITHMS | VARIATIONAL-INEQUALITIES | MATHEMATICS | PROJECTION | phi-Lipschitz-type continuity | CONVERGENCE THEOREMS | EQUILIBRIUM PROBLEMS | Algorithms | Equality | Analysis | Methods | Theorems | Banach spaces | Iterative methods | Banach space

Split equality equilibrium problem | Pseudomonotone bifunction | 47H10 | Variational inequality | Numerical Analysis | phi $$ ϕ -Lipschitz-type continuity | 47H09 | Mathematics | Theory of Computation | 47H05 | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | POINT PROBLEM | CONVEX FEASIBILITY | FEASIBILITY PROBLEM | ITERATIVE METHOD | ALGORITHMS | VARIATIONAL-INEQUALITIES | MATHEMATICS | PROJECTION | phi-Lipschitz-type continuity | CONVERGENCE THEOREMS | EQUILIBRIUM PROBLEMS | Algorithms | Equality | Analysis | Methods | Theorems | Banach spaces | Iterative methods | Banach space

Journal Article

15.
Full Text
Gradient Methods with Selection Technique for the Multiple-Sets Split Equality Problem

Mathematics, ISSN 2227-7390, 10/2019, Volume 7, Issue 10, p. 928

The inverse problem is one of the four major problems in computational mathematics. There is an inverse problem in medical image reconstruction and...

selection technique | split equality problem | multiple-sets split equality problem

selection technique | split equality problem | multiple-sets split equality problem

Journal Article

Calcolo, ISSN 0008-0624, 12/2018, Volume 55, Issue 4, pp. 1 - 31

The purpose of this paper is to introduce and study an iterative algorithm for solving a general split equality problem. The problem consists of finding a...

47H10 | Split equality optimization problems | Equilibrium problem | Numerical Analysis | Demimetric mapping | Split equality problems | Mathematics | Theory of Computation | 47J25 | 47N10 | 65J15 | HILBERT-SPACES | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | ALTERNATING PROXIMAL ALGORITHMS | CONVEX FEASIBILITY | ITERATIVE ALGORITHMS | RADIATION-THERAPY | MATHEMATICS | BANACH-SPACES | COMMON FIXED-POINT | VISCOSITY APPROXIMATION METHODS | MONOTONE-OPERATORS | Algorithms | Equality | Problems | Theorems | Fixed points (mathematics) | Iterative algorithms | Hilbert space | Optimization | Convergence

47H10 | Split equality optimization problems | Equilibrium problem | Numerical Analysis | Demimetric mapping | Split equality problems | Mathematics | Theory of Computation | 47J25 | 47N10 | 65J15 | HILBERT-SPACES | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | ALTERNATING PROXIMAL ALGORITHMS | CONVEX FEASIBILITY | ITERATIVE ALGORITHMS | RADIATION-THERAPY | MATHEMATICS | BANACH-SPACES | COMMON FIXED-POINT | VISCOSITY APPROXIMATION METHODS | MONOTONE-OPERATORS | Algorithms | Equality | Problems | Theorems | Fixed points (mathematics) | Iterative algorithms | Hilbert space | Optimization | Convergence

Journal Article

Journal of Applied Analysis, ISSN 1425-6908, 06/2016, Volume 22, Issue 1, pp. 81 - 89

In this paper, we studied the split equality problems (SEP) with a new proposed iterative algorithm and established the strong convergence of the proposed...

Split equality problem | relaxed projection algorithm | 47H09 | projection algorithm | 47J25 | Studies | Mathematics | Algorithms

Split equality problem | relaxed projection algorithm | 47H09 | projection algorithm | 47J25 | Studies | Mathematics | Algorithms

Journal Article

JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS, ISSN 2008-1898, 2017, Volume 10, Issue 6, pp. 3217 - 3230

In this paper, we present a new algorithm for the split equality problem for finding a common element of solution of equilibrium problem, solution of...

Split equality problem | ALTERNATING PROXIMAL ALGORITHMS | SET | CONVEX FEASIBILITY | equilibrium problem | variational inequality | ITERATIVE ALGORITHMS | MATHEMATICS | PROJECTION | fixed point | MAPPINGS | nonexpansive semigroups | OPERATORS | STRONG-CONVERGENCE

Split equality problem | ALTERNATING PROXIMAL ALGORITHMS | SET | CONVEX FEASIBILITY | equilibrium problem | variational inequality | ITERATIVE ALGORITHMS | MATHEMATICS | PROJECTION | fixed point | MAPPINGS | nonexpansive semigroups | OPERATORS | STRONG-CONVERGENCE

Journal Article

19.
Linear convergence of an iterative algorithm for solving the multiple-sets split equality problem

Journal of Nonlinear Functional Analysis, 2019, Volume 2019

Journal Article

Journal of Fixed Point Theory and Applications, ISSN 1661-7738, 3/2018, Volume 20, Issue 1, pp. 1 - 17

The purpose of this paper is to propose and study an algorithm for solving the general split equality problem governed by Bregman quasi-nonexpansive mappings...

duality mapping | Mathematics | uniformly smooth | strong convergence | uniformly convex | Mathematical Methods in Physics | 49J53 | Analysis | 47H09 | Mathematics, general | 65K10 | general split problems | 49M37 | 47H05 | Bregman quasi-nonexpansive mappings | FIXED-POINT PROBLEM | MATHEMATICS, APPLIED | STRONG-CONVERGENCE THEOREMS | ALGORITHMS | MATHEMATICS | CONVEX | EQUILIBRIUM | ITERATIVE METHODS | Algorithms | Equality

duality mapping | Mathematics | uniformly smooth | strong convergence | uniformly convex | Mathematical Methods in Physics | 49J53 | Analysis | 47H09 | Mathematics, general | 65K10 | general split problems | 49M37 | 47H05 | Bregman quasi-nonexpansive mappings | FIXED-POINT PROBLEM | MATHEMATICS, APPLIED | STRONG-CONVERGENCE THEOREMS | ALGORITHMS | MATHEMATICS | CONVEX | EQUILIBRIUM | ITERATIVE METHODS | Algorithms | Equality

Journal Article

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