It is well known that Newton and quasi-Newton algorithms are effective to small and medium scale smooth problems because they take full use of corresponding gradient function’s information but fail to solve nonsmooth...It is well known that Newton and quasi-Newton algorithms are effective to small and medium scale smooth problems because they take full use of corresponding gradient function’s information but fail to solve nonsmooth problems.The perfect algorithm stems from concept of‘bundle’successfully addresses both smooth and nonsmooth complex problems,but it is regrettable that it is merely effective to small and medium optimization models since it needs to store and update relevant information of parameter’s bundle.The conjugate gradient algorithm is effective both large-scale smooth and nonsmooth optimization model since its simplicity that utilizes objective function’s information and the technique of Moreau-Yosida regularization.Thus,a modified three-term conjugate gradient algorithm was proposed,and it has a sufficiently descent property and a trust region character.At the same time,it possesses the global convergence under mild assumptions and numerical test proves it is efficient than similar optimization algorithms.展开更多
Information networks are becoming increasingly important in practice. However, their escalating complexity is gradually impeding the efficiency of data mining. A novel network schema called the Behavior Schema of Info...Information networks are becoming increasingly important in practice. However, their escalating complexity is gradually impeding the efficiency of data mining. A novel network schema called the Behavior Schema of Information Networks (BSIN) is proposed to address this issue. This work defines the behavior of nodes as connected paths in BSIN, proposes a novel function distinguish behavior differences, and introduces approximate bisimulation into the acquisition of quotient sets for node types. The major highlight of BSIN is its ability to directly obtain a high-efficiency network on the basis of approximate bisimulation, rather than reducing the existing information network. It provides an effective representation of information networks, and the resulting novel network has a simple structure that more efficiently expresses semantic information than current network representations. The theoretical analysis of the connected paths between the original and the obtained networks demonstrates that errors are controllable;and semantic information is approximately retained. Case studies show that BSIN yields a simple network and is highly cost-effective.展开更多
基金This work is supported by the National Natural Science Foundation of China(Grant No.11661009)the Guangxi Science Fund for Distinguished Young Scholars(No.2015GXNSFGA139001)+1 种基金the Guangxi Natural Science Key Fund(No.2017GXNSFDA198046)Innovation Project of Guangxi Graduate Education(No.YCSW2018046).
文摘It is well known that Newton and quasi-Newton algorithms are effective to small and medium scale smooth problems because they take full use of corresponding gradient function’s information but fail to solve nonsmooth problems.The perfect algorithm stems from concept of‘bundle’successfully addresses both smooth and nonsmooth complex problems,but it is regrettable that it is merely effective to small and medium optimization models since it needs to store and update relevant information of parameter’s bundle.The conjugate gradient algorithm is effective both large-scale smooth and nonsmooth optimization model since its simplicity that utilizes objective function’s information and the technique of Moreau-Yosida regularization.Thus,a modified three-term conjugate gradient algorithm was proposed,and it has a sufficiently descent property and a trust region character.At the same time,it possesses the global convergence under mild assumptions and numerical test proves it is efficient than similar optimization algorithms.
基金supported by the National Natural Science Foundation of China(No.12261027)the Innovation Project of Guangxi Graduate Education(No.YCBZ2021027).
文摘Information networks are becoming increasingly important in practice. However, their escalating complexity is gradually impeding the efficiency of data mining. A novel network schema called the Behavior Schema of Information Networks (BSIN) is proposed to address this issue. This work defines the behavior of nodes as connected paths in BSIN, proposes a novel function distinguish behavior differences, and introduces approximate bisimulation into the acquisition of quotient sets for node types. The major highlight of BSIN is its ability to directly obtain a high-efficiency network on the basis of approximate bisimulation, rather than reducing the existing information network. It provides an effective representation of information networks, and the resulting novel network has a simple structure that more efficiently expresses semantic information than current network representations. The theoretical analysis of the connected paths between the original and the obtained networks demonstrates that errors are controllable;and semantic information is approximately retained. Case studies show that BSIN yields a simple network and is highly cost-effective.
