A hybridization of the three–term conjugate gradient method proposed by Zhang et al. and the nonlinear conjugate gradient method proposed by Polak and Ribi`ere, and Polyak is suggested. Based on an eigenvalue analysi...A hybridization of the three–term conjugate gradient method proposed by Zhang et al. and the nonlinear conjugate gradient method proposed by Polak and Ribi`ere, and Polyak is suggested. Based on an eigenvalue analysis, it is shown that search directions of the proposed method satisfy the sufficient descent condition, independent of the line search and the objective function convexity. Global convergence of the method is established under an Armijo–type line search condition. Numerical experiments show practical efficiency of the proposed method.展开更多
This paper concerns the problem of stabilizing fuzzy chaotic systems via the viewpoint of the edgewise subdivision approach. Firstly, a new edgewise subdivision algorithm is proposed to implement the simplex edgewise ...This paper concerns the problem of stabilizing fuzzy chaotic systems via the viewpoint of the edgewise subdivision approach. Firstly, a new edgewise subdivision algorithm is proposed to implement the simplex edgewise subdivision which divides the overall fuzzy chaotic systems into a lot of sub-systems by a kind of algebraic description. These sub-systems have the same volume and shape characteristics. Secondly, a novel kind of control scheme which switches by the transfer of different operating sub-systems is proposed to achieve convergent stabilization conditions for the underlying controlled fuzzy chaotic systems. Finally, a numerical example is given to demonstrate the validity of the proposed methods.展开更多
In the paper, a new mixed algorithm combined with schemes of nonmonotone line search, the systems of linear equations for higher order modification and sequential quadratic programming for constrained optimizations is...In the paper, a new mixed algorithm combined with schemes of nonmonotone line search, the systems of linear equations for higher order modification and sequential quadratic programming for constrained optimizations is presented. Under some weaker assumptions,without strict complementary condition, the algorithm is globally and superlinearly convergent.展开更多
Single SAR image direct positioning is to determine the ground coordinate for each pixel in the SAR image assisted with a reference DEM.During this procedure,an iterative procedure is essentially needed to solve the u...Single SAR image direct positioning is to determine the ground coordinate for each pixel in the SAR image assisted with a reference DEM.During this procedure,an iterative procedure is essentially needed to solve the uncertainty in elevation of each pixel in the SAR image.However,such an iterative procedure may suffer from the problem of divergence in shaded and serious layover areas.To investigate this problem,we performed a theoretical analysis on the convergence conditions that has not been intensively studied till now.The Range-Doppler(RD)model was simplified and then the general surface is degenerated into a planar surface.Mathematical deduction was then carried out to derive the convergence conditions and the impact factors for the convergence speed were evaluated.The theoretical findings were validated by experiments for both simulated and real scenarios.展开更多
The Landweber scheme is a method for algebraic image reconstructions. The convergence behavior of the Landweber scheme is of both theoretical and practical importance. Using the diagonalization of matrix, we derive a ...The Landweber scheme is a method for algebraic image reconstructions. The convergence behavior of the Landweber scheme is of both theoretical and practical importance. Using the diagonalization of matrix, we derive a neat iterative representation formula for the Landweber schemes and consequently establish the convergence conditions of Landweber iteration. This work refines our previous convergence results on the Landweber scheme.展开更多
Recently, Bourgat et al.[3] gave a domain decomposition algorithm which can be implemented in parallel, and many numerical experiments have illustrated its efficiency. In this paper,we make a detailed theoretical anal...Recently, Bourgat et al.[3] gave a domain decomposition algorithm which can be implemented in parallel, and many numerical experiments have illustrated its efficiency. In this paper,we make a detailed theoretical analysis about this algorithm.展开更多
The convergence properties of Newton's method for systems of equations with constant rank derivatives are studied under the hypothesis that the derivatives satisfy some weak Lipschitz conditions. The unified converge...The convergence properties of Newton's method for systems of equations with constant rank derivatives are studied under the hypothesis that the derivatives satisfy some weak Lipschitz conditions. The unified convergence results, which include Kantorovich type theorems and Smale's point estimate theorems as special cases, are obtained.展开更多
Since the point-to-set maps were introduced by Zangwill in the study of conceptual algorithms, various sufficient conditions for the algorithms to be of global convergence have been established.In this paper, the rela...Since the point-to-set maps were introduced by Zangwill in the study of conceptual algorithms, various sufficient conditions for the algorithms to be of global convergence have been established.In this paper, the relations among all these conditions are illustrated by a unified approach;still more, unlike the sufficient conditions previously given in the literature,a new necessary condition is put forward at the end of the paper, so that it implies more applications.展开更多
City growth patterns are attracting more attention in urban geography studies. This paper examines how cities develop and grow in the upper tail of size distribution in a large-scale economy based on a theoretical mod...City growth patterns are attracting more attention in urban geography studies. This paper examines how cities develop and grow in the upper tail of size distribution in a large-scale economy based on a theoretical model under new economic geography framework and the empirical evidence from the US. The results show that cities grow in a sequential pattern. Cities with the best economic conditions are the first to grow fastest until they reach a critical size, then their growth rates slow down and the smaller cities farther down in the urban hierarchy become the fastest-growing ones in sequence. This paper also reveals three related features of urban system. First, the city size distribution evolves from low-level balanced to primate and finally high-level balanced pattern in an inverted U-shaped path. Second, there exist persistent discontinuities, or gaps, between city size classes. Third, city size in the upper tail exhibits conditional convergence characteristics. This paper could not only contribute to enhancing the understanding of urbanization process and city size distribution dynamics, but also be widely used in making effective policies and scientific urban planning.展开更多
This paper proposes a new cooperative projection neural network (CPNN), which combines automatically three individual neural network models with a common projection term. As a special case, the proposed CPNN can inc...This paper proposes a new cooperative projection neural network (CPNN), which combines automatically three individual neural network models with a common projection term. As a special case, the proposed CPNN can include three recent recurrent neural networks for solving monotone variational inequality problems with limit or linear constraints, respectively. Under the monotonicity condition of the corresponding Lagrangian mapping, the proposed CPNN is theoretically guaranteed to solve monotone variational inequality problems and a class of nonmonotone variational inequality problems with linear and nonlinear constraints. Unlike the extended projection neural network, the proposed CPNN has no limitation on the initial point for global convergence. Compared with other related cooperative neural networks and numerical optimization algorithms, the proposed CPNN has a low computational complexity and requires weak convergence conditions. An application in real-time grasping force optimization and examples demonstrate good performance of the proposed CPNN.展开更多
基金Supported by Research Council of Semnan University
文摘A hybridization of the three–term conjugate gradient method proposed by Zhang et al. and the nonlinear conjugate gradient method proposed by Polak and Ribi`ere, and Polyak is suggested. Based on an eigenvalue analysis, it is shown that search directions of the proposed method satisfy the sufficient descent condition, independent of the line search and the objective function convexity. Global convergence of the method is established under an Armijo–type line search condition. Numerical experiments show practical efficiency of the proposed method.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.50977008,60774048 and 60821063)the Program for Cheung Kong Scholars and National Basic Research Program of China (Grant No.2009CB320601)
文摘This paper concerns the problem of stabilizing fuzzy chaotic systems via the viewpoint of the edgewise subdivision approach. Firstly, a new edgewise subdivision algorithm is proposed to implement the simplex edgewise subdivision which divides the overall fuzzy chaotic systems into a lot of sub-systems by a kind of algebraic description. These sub-systems have the same volume and shape characteristics. Secondly, a novel kind of control scheme which switches by the transfer of different operating sub-systems is proposed to achieve convergent stabilization conditions for the underlying controlled fuzzy chaotic systems. Finally, a numerical example is given to demonstrate the validity of the proposed methods.
文摘In the paper, a new mixed algorithm combined with schemes of nonmonotone line search, the systems of linear equations for higher order modification and sequential quadratic programming for constrained optimizations is presented. Under some weaker assumptions,without strict complementary condition, the algorithm is globally and superlinearly convergent.
基金The authors would like to thank the German Aerospace Center(DLR)for providing the test data-sets via the DLR AO LAN0793 and LAN0634,and Prof.Miaozhong Xu of LIESMARS for providing the photogrammetric DEM with spatial resolution of 3 mThis work was supported by the National Natural Science Foundation of China[grant number 41271457]the Demonstration System of High Resolution Remote Sensing Applications in Urban Fine Management Area[grant number 06-Y30B04–9002-13/15].
文摘Single SAR image direct positioning is to determine the ground coordinate for each pixel in the SAR image assisted with a reference DEM.During this procedure,an iterative procedure is essentially needed to solve the uncertainty in elevation of each pixel in the SAR image.However,such an iterative procedure may suffer from the problem of divergence in shaded and serious layover areas.To investigate this problem,we performed a theoretical analysis on the convergence conditions that has not been intensively studied till now.The Range-Doppler(RD)model was simplified and then the general surface is degenerated into a planar surface.Mathematical deduction was then carried out to derive the convergence conditions and the impact factors for the convergence speed were evaluated.The theoretical findings were validated by experiments for both simulated and real scenarios.
基金Supported by the National Natural Science Foundation of China(No.61071144,61271012,61121002,10990013)
文摘The Landweber scheme is a method for algebraic image reconstructions. The convergence behavior of the Landweber scheme is of both theoretical and practical importance. Using the diagonalization of matrix, we derive a neat iterative representation formula for the Landweber schemes and consequently establish the convergence conditions of Landweber iteration. This work refines our previous convergence results on the Landweber scheme.
文摘Recently, Bourgat et al.[3] gave a domain decomposition algorithm which can be implemented in parallel, and many numerical experiments have illustrated its efficiency. In this paper,we make a detailed theoretical analysis about this algorithm.
基金Acknowledgments. This work was supported in part by the National Natural Science Foundation of China (Grant No. 10671175) and Program for New Century Excellent Talents in Universities. The first author was also supported in part by the Education Ministry of Zhejiang Province (Grant No. 20060492).
文摘The convergence properties of Newton's method for systems of equations with constant rank derivatives are studied under the hypothesis that the derivatives satisfy some weak Lipschitz conditions. The unified convergence results, which include Kantorovich type theorems and Smale's point estimate theorems as special cases, are obtained.
文摘Since the point-to-set maps were introduced by Zangwill in the study of conceptual algorithms, various sufficient conditions for the algorithms to be of global convergence have been established.In this paper, the relations among all these conditions are illustrated by a unified approach;still more, unlike the sufficient conditions previously given in the literature,a new necessary condition is put forward at the end of the paper, so that it implies more applications.
基金National Natural Science Foundation of China,No.41230632 Key Project for the Strategic Science Plan in IGSNRR,CAS,No.2012ZD006
文摘City growth patterns are attracting more attention in urban geography studies. This paper examines how cities develop and grow in the upper tail of size distribution in a large-scale economy based on a theoretical model under new economic geography framework and the empirical evidence from the US. The results show that cities grow in a sequential pattern. Cities with the best economic conditions are the first to grow fastest until they reach a critical size, then their growth rates slow down and the smaller cities farther down in the urban hierarchy become the fastest-growing ones in sequence. This paper also reveals three related features of urban system. First, the city size distribution evolves from low-level balanced to primate and finally high-level balanced pattern in an inverted U-shaped path. Second, there exist persistent discontinuities, or gaps, between city size classes. Third, city size in the upper tail exhibits conditional convergence characteristics. This paper could not only contribute to enhancing the understanding of urbanization process and city size distribution dynamics, but also be widely used in making effective policies and scientific urban planning.
基金Supported by the National Natural Science Foundation of China (Grant No. 60875085)the Natural Science Foundation of Fujian Province(Grant No. 2008J0019)
文摘This paper proposes a new cooperative projection neural network (CPNN), which combines automatically three individual neural network models with a common projection term. As a special case, the proposed CPNN can include three recent recurrent neural networks for solving monotone variational inequality problems with limit or linear constraints, respectively. Under the monotonicity condition of the corresponding Lagrangian mapping, the proposed CPNN is theoretically guaranteed to solve monotone variational inequality problems and a class of nonmonotone variational inequality problems with linear and nonlinear constraints. Unlike the extended projection neural network, the proposed CPNN has no limitation on the initial point for global convergence. Compared with other related cooperative neural networks and numerical optimization algorithms, the proposed CPNN has a low computational complexity and requires weak convergence conditions. An application in real-time grasping force optimization and examples demonstrate good performance of the proposed CPNN.