An ε-subgradient projection algorithm for solving a convex feasibility problem is presented.Based on the iterative projection methods and the notion of ε-subgradient,a series of special projection hyperplanes is est...An ε-subgradient projection algorithm for solving a convex feasibility problem is presented.Based on the iterative projection methods and the notion of ε-subgradient,a series of special projection hyperplanes is established.Moreover,compared with the existing projection hyperplanes methods with subgradient,the proposed hyperplanes are interactive with ε,and their ranges are more larger.The convergence of the proposed algorithm is given under some mild conditions,and the validity of the algorithm is proved by the numerical test.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
The existing methods of projection for solving convex feasibility problem may lead to slow conver- gence when the sequences enter some narrow＂corridor＂ between two or more convex sets. In this paper, we apply a tech...The existing methods of projection for solving convex feasibility problem may lead to slow conver- gence when the sequences enter some narrow＂corridor＂ between two or more convex sets. In this paper, we apply a technique that may interrupt the monotonity of the constructed sequence to the sequential subgradient pro- jection algorithm to construct a nommonotonous sequential subgradient projection algorithm for solving convex feasibility problem, which can leave such corridor by taking a big step at different steps during the iteration. Under some suitable conditions, the convergence is proved.We also compare the numerical performance of the proposed algorithm with that of the monotonous algorithm by numerical experiments.展开更多
With the development of the compressive sensing theory, the image reconstruction from the projections viewed in limited angles is one of the hot problems in the research of computed tomography technology. This paper d...With the development of the compressive sensing theory, the image reconstruction from the projections viewed in limited angles is one of the hot problems in the research of computed tomography technology. This paper develops an iterative algorithm for image reconstruction, which can fit the most cases. This method gives an image reconstruction flow with the difference image vector, which is based on the concept that the difference image vector between the reconstructed and the reference image is sparse enough. Then the l1-norm minimization method is used to reconstruct the difference vector to recover the image for flat subjects in limited angles. The algorithm has been tested with a thin planar phantom and a real object in limited-view projection data. Moreover, all the studies showed the satisfactory results in accuracy at a rather high reconstruction speed.展开更多
In this paper we investigate several solution algorithms for the convex fea- sibility problem(CFP)and the best approximation problem(BAP)respectively.The algorithms analyzed are already known before,but by adequately ...In this paper we investigate several solution algorithms for the convex fea- sibility problem(CFP)and the best approximation problem(BAP)respectively.The algorithms analyzed are already known before,but by adequately reformulating the CFP or the BAP we naturally deduce the general projection method for the CFP from well-known steepest decent method for unconstrained optimization and we also give a natural strategy of updating weight parameters.In the linear case we show the connec- tion of the two projection algorithms for the CFP and the BAP respectively.In addition, we establish the convergence of a method for the BAP under milder assumptions in the linear case.We also show by examples a Bauschke's conjecture is only partially correct.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
基金supported by the National Natural Science Foundation of China (10671126)Shanghai Leading Academic Discipline Project(S30501)
文摘An ε-subgradient projection algorithm for solving a convex feasibility problem is presented.Based on the iterative projection methods and the notion of ε-subgradient,a series of special projection hyperplanes is established.Moreover,compared with the existing projection hyperplanes methods with subgradient,the proposed hyperplanes are interactive with ε,and their ranges are more larger.The convergence of the proposed algorithm is given under some mild conditions,and the validity of the algorithm is proved by the numerical test.
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 the National Science Foundation of China(No.11171221)Natural Science Foundation of Shanghai(14ZR1429200)+2 种基金Innovation Program of Shanghai Municipal Education Commission(15ZZ074)Henan Province fundation frontier projec(No.162300410226)Key Scientific research projectins of Henan Province(NO.17b120001)
文摘The existing methods of projection for solving convex feasibility problem may lead to slow conver- gence when the sequences enter some narrow＂corridor＂ between two or more convex sets. In this paper, we apply a technique that may interrupt the monotonity of the constructed sequence to the sequential subgradient pro- jection algorithm to construct a nommonotonous sequential subgradient projection algorithm for solving convex feasibility problem, which can leave such corridor by taking a big step at different steps during the iteration. Under some suitable conditions, the convergence is proved.We also compare the numerical performance of the proposed algorithm with that of the monotonous algorithm by numerical experiments.
基金Project supported by the National Basic Research Program of China(Grant No.2006CB7057005)the National High Technology Research and Development Program of China(Grant No.2009AA012200)the National Natural Science Foundation of China (Grant No.60672104)
文摘With the development of the compressive sensing theory, the image reconstruction from the projections viewed in limited angles is one of the hot problems in the research of computed tomography technology. This paper develops an iterative algorithm for image reconstruction, which can fit the most cases. This method gives an image reconstruction flow with the difference image vector, which is based on the concept that the difference image vector between the reconstructed and the reference image is sparse enough. Then the l1-norm minimization method is used to reconstruct the difference vector to recover the image for flat subjects in limited angles. The algorithm has been tested with a thin planar phantom and a real object in limited-view projection data. Moreover, all the studies showed the satisfactory results in accuracy at a rather high reconstruction speed.
基金supported by the National Natural Science Foundation of China,Grant 10571134
文摘In this paper we investigate several solution algorithms for the convex fea- sibility problem(CFP)and the best approximation problem(BAP)respectively.The algorithms analyzed are already known before,but by adequately reformulating the CFP or the BAP we naturally deduce the general projection method for the CFP from well-known steepest decent method for unconstrained optimization and we also give a natural strategy of updating weight parameters.In the linear case we show the connec- tion of the two projection algorithms for the CFP and the BAP respectively.In addition, we establish the convergence of a method for the BAP under milder assumptions in the linear case.We also show by examples a Bauschke's conjecture is only partially correct.
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The National Natural Science Foundation of China(11171221)the Science and Technology of Shanghai Municipal Committee(10550500800)the Leading Academic Discipline Project of Shanghai(S30501)
