A Relaxed Self-Adaptive Projection Algorithm for Solving the Multiple-Sets Split Equality Problem

In this article, we introduce a relaxed self-adaptive projection algorithm for solving the multiple-sets split equality problem. Firstly, we transfer the original problem to the constrained multiple-sets split equality problem and a fixed point equation system is established. Then, we show the equivalence of the constrained multiple-sets split equality problem and the fixed point equation system. Secondly, we present a relaxed self-adaptive projection algorithm for the fixed point equation system. The advantage of the self-adaptive step size is that it could be obtained directly from the iterative procedure. Furthermore, we prove the convergence of the proposed algorithm. Finally, several numerical results are shown to confirm the feasibility and efficiency of the proposed algorithm.

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Iterative algorithm for solving the multiple-sets split equality problem with split self-adaptive step size in Hilbert spaces

Journal of Inequalities and Applications ◽

10.1186/s13660-016-0982-7 ◽

2016 ◽

Vol 2016 (1) ◽

Cited By ~ 2

Author(s):

Dianlu Tian ◽

Luoyi Shi ◽

Rudong Chen

Keyword(s):

Iterative Algorithm ◽

Hilbert Spaces ◽

Step Size ◽

Split Equality Problem ◽

Adaptive Step Size ◽

Equality Problem ◽

Adaptive Step ◽

Self Adaptive

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An accelerated hybrid projection method with a self-adaptive step-size sequence for solving split common fixed point problems

Authorea ◽

10.22541/au.158801025.57920103 ◽

2020 ◽

Author(s):

Zheng Zhou ◽

Bing Tan ◽

Songxiao Li

Keyword(s):

Fixed Point ◽

Common Fixed Point ◽

Projection Method ◽

Fixed Point Problems ◽

Step Size ◽

Adaptive Step Size ◽

Hybrid Projection Method ◽

Split Common Fixed Point ◽

Adaptive Step ◽

Self Adaptive

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Inertial shrinking projection algorithm with self-adaptive step size for split generalized equilibrium and fixed point problems for a countable family of nonexpansive multivalued mappings

Demonstratio Mathematica ◽

10.1515/dema-2021-0006 ◽

2021 ◽

Vol 54 (1) ◽

pp. 47-67

Author(s):

Musa A. Olona ◽

Timilehin O. Alakoya ◽

Abd-semii O.-E. Owolabi ◽

Oluwatosin T. Mewomo

Keyword(s):

Countable Family ◽

Projection Algorithm ◽

Common Element ◽

Multivalued Mappings ◽

Strong Convergence Theorem ◽

Step Size ◽

Adaptive Step Size ◽

Generalized Equilibrium ◽

Adaptive Step ◽

Self Adaptive

Abstract In this paper, we introduce a shrinking projection method of an inertial type with self-adaptive step size for finding a common element of the set of solutions of a split generalized equilibrium problem and the set of common fixed points of a countable family of nonexpansive multivalued mappings in real Hilbert spaces. The self-adaptive step size incorporated helps to overcome the difficulty of having to compute the operator norm, while the inertial term accelerates the rate of convergence of the proposed algorithm. Under standard and mild conditions, we prove a strong convergence theorem for the problems under consideration and obtain some consequent results. Finally, we apply our result to solve split mixed variational inequality and split minimization problems, and we present numerical examples to illustrate the efficiency of our algorithm in comparison with other existing algorithms. Our results complement and generalize several other results in this direction in the current literature.

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An Inertial Generalized Viscosity Approximation Method for Solving Multiple-Sets Split Feasibility Problems and Common Fixed Point of Strictly Pseudo-Nonspreading Mappings

Axioms ◽

10.3390/axioms10010001 ◽

2020 ◽

Vol 10 (1) ◽

pp. 1

Author(s):

Hammed Anuoluwapo Abass ◽

Lateef Olakunle Jolaoso

Keyword(s):

Fixed Point ◽

Approximation Method ◽

Feasibility Problem ◽

Viscosity Approximation Method ◽

Viscosity Approximation ◽

Step Size ◽

Adaptive Step Size ◽

Adaptive Step ◽

Split Feasibility ◽

Self Adaptive

In this paper, we propose a generalized viscosity iterative algorithm which includes a sequence of contractions and a self adaptive step size for approximating a common solution of a multiple-set split feasibility problem and fixed point problem for countable families of k-strictly pseudononspeading mappings in the framework of real Hilbert spaces. The advantage of the step size introduced in our algorithm is that it does not require the computation of the Lipschitz constant of the gradient operator which is very difficult in practice. We also introduce an inertial process version of the generalize viscosity approximation method with self adaptive step size. We prove strong convergence results for the sequences generated by the algorithms for solving the aforementioned problems and present some numerical examples to show the efficiency and accuracy of our algorithm. The results presented in this paper extends and complements many recent results in the literature.

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Internal Perturbation Projection Algorithm for the Extended Split Equality Problem and the Extended Split Equality Fixed Point Problem

Journal of Function Spaces ◽

10.1155/2020/6034754 ◽

2020 ◽

Vol 2020 ◽

pp. 1-15

Author(s):

Meixia Li ◽

Xueling Zhou ◽

Wenchao Wang

Keyword(s):

Fixed Point ◽

Iterative Algorithms ◽

Nonlinear Problems ◽

Fixed Point Problem ◽

Projection Algorithm ◽

Feasibility Problem ◽

Point Problem ◽

Split Equality Problem ◽

Equality Problem ◽

Internal Perturbation

In this article, we study the extended split equality problem and extended split equality fixed point problem, which are extensions of the convex feasibility problem. For solving the extended split equality problem, we present two self-adaptive stepsize algorithms with internal perturbation projection and obtain the weak and the strong convergence of the algorithms, respectively. Furthermore, based on the operators being quasinonexpansive, we offer an iterative algorithm to solve the extended split equality fixed point problem. We introduce a way of selecting the stepsize which does not need any prior information about operator norms in the three algorithms. We apply our iterative algorithms to some convex and nonlinear problems. Finally, several numerical results are shown to confirm the feasibility and efficiency of the proposed algorithms.

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