By using Fukushima's differentiable merit function,Taji,Fukushima and Ibaraki have given a globally convergent modified Newton method for the strongly monotone variational inequality problem and proved their metho...By using Fukushima's differentiable merit function,Taji,Fukushima and Ibaraki have given a globally convergent modified Newton method for the strongly monotone variational inequality problem and proved their method to be quadratically convergent under certain assumptions in 1993.In this paper a hybrid method for the variational inequality problem under the assumptions that the mapping F is continuously differentiable and its Jacobian matrix Δ F(x) is positive definite for all x∈S rather than strongly monotone and that the set S is nonempty,polyhedral,closed and convex is proposed.Armijo type line search and trust region strategies as well as Fukushima's differentiable merit function are incorporated into the method.It is then shown that the method is well defined and globally convergent and that,under the same assumptions as those of Taji et al.,the method reduces to the basic Newton method and hence the rate of convergence is quadratic.Computational experiences show the efficiency of the proposed method.展开更多
In this paper, an algorithm for unconstrained optimization that employs both trust region techniques and curvilinear searches is proposed. At every iteration, we solve the trust region subproblem whose radius is gener...In this paper, an algorithm for unconstrained optimization that employs both trust region techniques and curvilinear searches is proposed. At every iteration, we solve the trust region subproblem whose radius is generated adaptively only once. Nonmonotonic backtracking curvilinear searches are performed when the solution of the subproblem is unacceptable. The global convergence and fast local convergence rate of the proposed algorithms are established under some reasonable conditions. The results of numerical ＇experiments are reported to show the effectiveness of the proposed algorithms.展开更多
We consider the problem of finding map regions that best match query keywords. This region search problem can be applied in many practical scenarios such as shopping recommendation, searching for tourist attractions, ...We consider the problem of finding map regions that best match query keywords. This region search problem can be applied in many practical scenarios such as shopping recommendation, searching for tourist attractions, and collision region detection for wireless sensor networks. While conventional map search retrieves isolate locations in a map, users frequently attempt to find regions of interest instead, e.g., detecting regions having too many wireless sensors to avoid collision, or finding shopping areas featuring various merchandise or tourist attractions of different styles. Finding regions of interest in a map is a non-trivial problem and retrieving regions of arbitrary shapes poses particular challenges. In this paper, we present a novel region search algorithm, dense region search(DRS), and its extensions, to find regions of interest by estimating the density of locations containing the query keywords in the region. Experiments on both synthetic and real-world datasets demonstrate the effectiveness of our algorithm.展开更多
基金Project supported by the National Natural Science Foundation of China (1 9971 0 65)
文摘By using Fukushima's differentiable merit function,Taji,Fukushima and Ibaraki have given a globally convergent modified Newton method for the strongly monotone variational inequality problem and proved their method to be quadratically convergent under certain assumptions in 1993.In this paper a hybrid method for the variational inequality problem under the assumptions that the mapping F is continuously differentiable and its Jacobian matrix Δ F(x) is positive definite for all x∈S rather than strongly monotone and that the set S is nonempty,polyhedral,closed and convex is proposed.Armijo type line search and trust region strategies as well as Fukushima's differentiable merit function are incorporated into the method.It is then shown that the method is well defined and globally convergent and that,under the same assumptions as those of Taji et al.,the method reduces to the basic Newton method and hence the rate of convergence is quadratic.Computational experiences show the efficiency of the proposed method.
基金This work was supported by the National Natural Science Foundation of China （grant No. 10231060）, the Specialized Research Fund of Doctoral Program of Higher Education of China at No,20040319003 and the Graduates＇ Creative Project of Jiangsu Province, China,
文摘In this paper, an algorithm for unconstrained optimization that employs both trust region techniques and curvilinear searches is proposed. At every iteration, we solve the trust region subproblem whose radius is generated adaptively only once. Nonmonotonic backtracking curvilinear searches are performed when the solution of the subproblem is unacceptable. The global convergence and fast local convergence rate of the proposed algorithms are established under some reasonable conditions. The results of numerical ＇experiments are reported to show the effectiveness of the proposed algorithms.
基金supported by the Zhejiang Provincial Natural Science Foundation of China(No.LZ13F020001)the National Natural Science Foundation of China(Nos.61173185 and 61173186)+1 种基金the National Key Technology R&D Program of China(No.2012BAI34B01)the Hangzhou S&T Development Plan(No.20150834M22)
文摘We consider the problem of finding map regions that best match query keywords. This region search problem can be applied in many practical scenarios such as shopping recommendation, searching for tourist attractions, and collision region detection for wireless sensor networks. While conventional map search retrieves isolate locations in a map, users frequently attempt to find regions of interest instead, e.g., detecting regions having too many wireless sensors to avoid collision, or finding shopping areas featuring various merchandise or tourist attractions of different styles. Finding regions of interest in a map is a non-trivial problem and retrieving regions of arbitrary shapes poses particular challenges. In this paper, we present a novel region search algorithm, dense region search(DRS), and its extensions, to find regions of interest by estimating the density of locations containing the query keywords in the region. Experiments on both synthetic and real-world datasets demonstrate the effectiveness of our algorithm.
