This paper deals with a bi-extrapolated subgradient projection algorithm by intro- ducing two extrapolated factors in the iterative step to solve the multiple-sets split feasibility problem. The strategy is intend to ...This paper deals with a bi-extrapolated subgradient projection algorithm by intro- ducing two extrapolated factors in the iterative step to solve the multiple-sets split feasibility problem. The strategy is intend to improve the convergence. And its convergence is proved un- der some suitable conditions. Numerical results illustrate that the bi-extrapolated subgradient projection algorithm converges more quickly than the existing algorithms.展开更多
In this paper,we introduce an inexact averaged projection algorithm to solve the nonconvex multiple-set split feasibility problem,where the involved sets are semi-algebraic proxregular sets.By means of the well-known ...In this paper,we introduce an inexact averaged projection algorithm to solve the nonconvex multiple-set split feasibility problem,where the involved sets are semi-algebraic proxregular sets.By means of the well-known Kurdyka-Lojasiewicz inequality,we establish the convergence of the proposed algorithm.展开更多
The purpose of this paper is to study and analyze an iterative method for finding a common element of the solution set ~ of the split feasibility problem and the set F（T） of fixed points of a right Bregman strongly ...The purpose of this paper is to study and analyze an iterative method for finding a common element of the solution set ~ of the split feasibility problem and the set F（T） of fixed points of a right Bregman strongly nonexpansive mapping T in the setting of p- uniformly convex Banach spaces which are also uniformly smooth. By combining Mann＇s iterative method and the Halpern＇s approximation method, we propose an iterative algorithm for finding an element of the set F（T）∩Ω moreover, we derive the strong convergence of the proposed algorithm under appropriate conditions and give numerical results to verify the efficiency and implementation of our method. Our results extend and complement many known related results in the literature.展开更多
The purpose of this article is to introduce a general split feasibility problems for two families of nonexpansive mappings in Hilbert spaces. We prove that the sequence generated by the proposed new algorithm converge...The purpose of this article is to introduce a general split feasibility problems for two families of nonexpansive mappings in Hilbert spaces. We prove that the sequence generated by the proposed new algorithm converges strongly to a solution of the general split feasibility problem. Our results extend and improve some recent known results.展开更多
In this paper, we propose two hybrid inertial CQ projection algorithms with linesearch process for the split feasibility problem. Based on the hybrid CQ projection algorithm, we firstly add the inertial term into the ...In this paper, we propose two hybrid inertial CQ projection algorithms with linesearch process for the split feasibility problem. Based on the hybrid CQ projection algorithm, we firstly add the inertial term into the iteration to accelerate the convergence of the algorithm, and adopt flexible rules for selecting the stepsize and the shrinking projection region, which makes an optimal stepsize available at each iteration. The shrinking projection region is the intersection of three sets, which are the set C and two hyperplanes. Furthermore, we modify the Armijo-type line-search step in the presented algorithm to get a new algorithm.The algorithms are shown to be convergent under certain mild assumptions. Besides, numerical examples are given to show that the proposed algorithms have better performance than the general CQ algorithm.展开更多
This paper studies the problem of split convex feasibility and a strong convergent alternating algorithm is established.According to this algorithm,some strong convergent theorems are obtained and an affirmative answe...This paper studies the problem of split convex feasibility and a strong convergent alternating algorithm is established.According to this algorithm,some strong convergent theorems are obtained and an affirmative answer to the question raised by Moudafi is given.At the same time,this paper also generalizes the problem of split convex feasibility.展开更多
In this paper,by combining the inertial technique and the gradient descent method with Polyak's stepsizes,we propose a novel inertial self-adaptive gradient algorithm to solve the split feasi-bility problem in Hil...In this paper,by combining the inertial technique and the gradient descent method with Polyak's stepsizes,we propose a novel inertial self-adaptive gradient algorithm to solve the split feasi-bility problem in Hilbert spaces and prove some strong and weak convergence theorems of our method under standard assumptions.We examine the performance of our method on the sparse recovery prob-lem beside an example in an infinite dimensional Hilbert space with synthetic data and give some numerical results to show the potential applicability of the proposed method and comparisons with related methods emphasize it further.展开更多
This paper considers the tensor split feasibility problem.Let C and Q be non-empty closed convex set and A be a semi-symmetric tensor.The tensor split feasibility problem is to find x∈C such that Axm−1∈Q.If we simpl...This paper considers the tensor split feasibility problem.Let C and Q be non-empty closed convex set and A be a semi-symmetric tensor.The tensor split feasibility problem is to find x∈C such that Axm−1∈Q.If we simply take this problem as a special case of the nonlinear split feasibility problem,then we can directly get a projection method to solve it.However,applying this kind of projection method to solve the tensor split feasibility problem is not so efficient.So we propose a Levenberg–Marquardt method to achieve higher efficiency.Theoretical analyses are conducted,and some preliminary numerical results show that the Levenberg–Marquardt method has advantage over the common projection method.展开更多
基金Supported by Natural Science Foundation of Shanghai(14ZR1429200)National Science Foundation of China(11171221)+4 种基金Shanghai Leading Academic Discipline Project(XTKX2012)Innovation Program of Shanghai Municipal Education Commission(14YZ094)Doctoral Program Foundation of Institutions of Higher Educationof China(20123120110004)Doctoral Starting Projection of the University of Shanghai for Science and Technology(ID-10-303-002)Young Teacher Training Projection Program of Shanghai for Science and Technology
文摘This paper deals with a bi-extrapolated subgradient projection algorithm by intro- ducing two extrapolated factors in the iterative step to solve the multiple-sets split feasibility problem. The strategy is intend to improve the convergence. And its convergence is proved un- der some suitable conditions. Numerical results illustrate that the bi-extrapolated subgradient projection algorithm converges more quickly than the existing algorithms.
基金Supported by the Natural Natural Science Foundation of China(Grant Nos.11801455,11971238)China Postdoctoral Science Foundation(Grant No.2019M663459)+1 种基金the Applied Basic Project of Sichuan Province(Grant No.20YYJC2523)the Fundamental Research Funds of China West Normal University(Grant Nos.17E084,18B031)。
文摘In this paper,we introduce an inexact averaged projection algorithm to solve the nonconvex multiple-set split feasibility problem,where the involved sets are semi-algebraic proxregular sets.By means of the well-known Kurdyka-Lojasiewicz inequality,we establish the convergence of the proposed algorithm.
文摘The purpose of this paper is to study and analyze an iterative method for finding a common element of the solution set ~ of the split feasibility problem and the set F（T） of fixed points of a right Bregman strongly nonexpansive mapping T in the setting of p- uniformly convex Banach spaces which are also uniformly smooth. By combining Mann＇s iterative method and the Halpern＇s approximation method, we propose an iterative algorithm for finding an element of the set F（T）∩Ω moreover, we derive the strong convergence of the proposed algorithm under appropriate conditions and give numerical results to verify the efficiency and implementation of our method. Our results extend and complement many known related results in the literature.
基金Supported by the Scientific Research Fund of Sichuan Provincial Department of Science and Technology(2015JY0165,2011JYZ011)the Scientific Research Fund of Sichuan Provincial Education Department(14ZA0271)+2 种基金the Scientific Research Project of Yibin University(2013YY06)the Natural Science Foundation of China Medical University,Taiwanthe National Natural Science Foundation of China(11361070)
文摘The purpose of this article is to introduce a general split feasibility problems for two families of nonexpansive mappings in Hilbert spaces. We prove that the sequence generated by the proposed new algorithm converges strongly to a solution of the general split feasibility problem. Our results extend and improve some recent known results.
基金Supported by the National Natural Science Foundation of China(72071130)。
文摘In this paper, we propose two hybrid inertial CQ projection algorithms with linesearch process for the split feasibility problem. Based on the hybrid CQ projection algorithm, we firstly add the inertial term into the iteration to accelerate the convergence of the algorithm, and adopt flexible rules for selecting the stepsize and the shrinking projection region, which makes an optimal stepsize available at each iteration. The shrinking projection region is the intersection of three sets, which are the set C and two hyperplanes. Furthermore, we modify the Armijo-type line-search step in the presented algorithm to get a new algorithm.The algorithms are shown to be convergent under certain mild assumptions. Besides, numerical examples are given to show that the proposed algorithms have better performance than the general CQ algorithm.
基金Supported by National Natural Science Foundation of China(Grant No.61174039)the Natural Science Foundation of Yunnan Province(Grant No.2010ZC152)the Candidate Foundation of Youth Academic Experts at Honghe University(Grant No.2014HB0206)
文摘This paper studies the problem of split convex feasibility and a strong convergent alternating algorithm is established.According to this algorithm,some strong convergent theorems are obtained and an affirmative answer to the question raised by Moudafi is given.At the same time,this paper also generalizes the problem of split convex feasibility.
基金funded by University of Transport and Communications (UTC) under Grant Number T2023-CB-001
文摘In this paper,by combining the inertial technique and the gradient descent method with Polyak's stepsizes,we propose a novel inertial self-adaptive gradient algorithm to solve the split feasi-bility problem in Hilbert spaces and prove some strong and weak convergence theorems of our method under standard assumptions.We examine the performance of our method on the sparse recovery prob-lem beside an example in an infinite dimensional Hilbert space with synthetic data and give some numerical results to show the potential applicability of the proposed method and comparisons with related methods emphasize it further.
基金the National Natural Science Foundation of China(Nos.11101028 and 11271206)National Key R&D Program of China(No.2017YFF0207401)the Fundamental Research Funds for the Central Universities(No.FRF-DF-19-004).
文摘This paper considers the tensor split feasibility problem.Let C and Q be non-empty closed convex set and A be a semi-symmetric tensor.The tensor split feasibility problem is to find x∈C such that Axm−1∈Q.If we simply take this problem as a special case of the nonlinear split feasibility problem,then we can directly get a projection method to solve it.However,applying this kind of projection method to solve the tensor split feasibility problem is not so efficient.So we propose a Levenberg–Marquardt method to achieve higher efficiency.Theoretical analyses are conducted,and some preliminary numerical results show that the Levenberg–Marquardt method has advantage over the common projection method.
基金The National Natural Science Foundation of China(1117122161403255)+6 种基金the Doctoral Program Foundation of Institutions of Higher Education of China(20123120110004)the China Coal Industry Association 2011 Annual Scientific and Technical Guidance Programs(MTKJ-2011-404)the Natural Science Foundation of Shanghai(14ZR1429200)the Shanghai Leading Academic Discipline Project(XTK X2012)the Innovation Program of Shanghai Municipal Education Commission(15ZZ073)the Doctoral Starting Projection of the University of Shanghai for Science and Technology(ID-10-303-002)the Young Teacher Training Projection Program of Shanghai for Science and Technology
