In this paper,the authors consider distributed convex optimization over hierarchical networks.The authors exploit the hierarchical architecture to design specialized distributed algorithms so that the complexity can b...In this paper,the authors consider distributed convex optimization over hierarchical networks.The authors exploit the hierarchical architecture to design specialized distributed algorithms so that the complexity can be reduced compared with that of non-hierarchically distributed algorithms.To this end,the authors use local agents to process local functions in the same manner as other distributed algorithms that take advantage of multiple agents'computing resources.Moreover,the authors use pseudocenters to directly integrate lower-level agents'computation results in each iteration step and then share the outcomes through the higher-level network formed by pseudocenters.The authors prove that the complexity of the proposed algorithm exponentially decreases with respect to the total number of pseudocenters.To support the proposed decomposition-composition method for agents and pseudocenters,the authors develop a class of operators.These operators are generalizations of the widely-used subgradient based operator and the proximal operator and can be used in distributed convex optimization.Additionally,these operators are closed with respect to the addition and composition operations;thus,they are suitable to guide hierarchically distributed design and analysis.Furthermore,these operators make the algorithm flexible since agents with different local functions can adopt suitable operators to simplify their calculations.Finally,numerical examples also illustrate the effectiveness of the method.展开更多
A large number of research results show that the synchronizability of complex networks is closely related to the topological structure. Some typical complex network models, such as random networks, small-world network...A large number of research results show that the synchronizability of complex networks is closely related to the topological structure. Some typical complex network models, such as random networks, small-world networks, BA scale-free network, etc, have totally different synchronizability. In this paper, a kind of hierarchical network synchronizability of self-similar module structures was studied, with more focus on the effect of the initial size of the module and network layer to the synchronizability and further research on the problem of network synchronous optimization. The Law of Segmentation Method was employed to reduce the maximum node betweenness and the Law of Parallel Reconnection employed to improve the ability of synchronizability of complex network by reducing the average path length of networks. Meanwhile, the effectiveness of proposed methods was verified through a lot of numerically simulative experiments.展开更多
This paper posits the desirability of a shift towards a holistic approach over reductionist approaches in the understanding of complex phenomena encountered in science and engineering. An argument based on set theory ...This paper posits the desirability of a shift towards a holistic approach over reductionist approaches in the understanding of complex phenomena encountered in science and engineering. An argument based on set theory is used to analyze three examples that illustrate the shortcomings of the reductionist approach. Using these cases as motivational points, a holistic approach to understand complex phenomena is proposed, whereby the human brain acts as a template to do so. Recognizing the need to maintain the transparency of the analysis provided by reductionism, a promising computational approach is offered by which the brain is used as a template for understanding complex phenomena. Some of the details of implementing this approach are also addressed.展开更多
基金supported in part by the National Key Research and Development Program of China under Grant No.2022YFA1004700in part by the Natural Science Foundation of China under Grant No.72171171in part by Shanghai Municipal Science and Technology Major Project under Grant No.2021SHZDZX0100。
文摘In this paper,the authors consider distributed convex optimization over hierarchical networks.The authors exploit the hierarchical architecture to design specialized distributed algorithms so that the complexity can be reduced compared with that of non-hierarchically distributed algorithms.To this end,the authors use local agents to process local functions in the same manner as other distributed algorithms that take advantage of multiple agents'computing resources.Moreover,the authors use pseudocenters to directly integrate lower-level agents'computation results in each iteration step and then share the outcomes through the higher-level network formed by pseudocenters.The authors prove that the complexity of the proposed algorithm exponentially decreases with respect to the total number of pseudocenters.To support the proposed decomposition-composition method for agents and pseudocenters,the authors develop a class of operators.These operators are generalizations of the widely-used subgradient based operator and the proximal operator and can be used in distributed convex optimization.Additionally,these operators are closed with respect to the addition and composition operations;thus,they are suitable to guide hierarchically distributed design and analysis.Furthermore,these operators make the algorithm flexible since agents with different local functions can adopt suitable operators to simplify their calculations.Finally,numerical examples also illustrate the effectiveness of the method.
文摘A large number of research results show that the synchronizability of complex networks is closely related to the topological structure. Some typical complex network models, such as random networks, small-world networks, BA scale-free network, etc, have totally different synchronizability. In this paper, a kind of hierarchical network synchronizability of self-similar module structures was studied, with more focus on the effect of the initial size of the module and network layer to the synchronizability and further research on the problem of network synchronous optimization. The Law of Segmentation Method was employed to reduce the maximum node betweenness and the Law of Parallel Reconnection employed to improve the ability of synchronizability of complex network by reducing the average path length of networks. Meanwhile, the effectiveness of proposed methods was verified through a lot of numerically simulative experiments.
基金sponsored by Prof. Dimitri Mavris and the Aerospace Systems Design Laboratory
文摘This paper posits the desirability of a shift towards a holistic approach over reductionist approaches in the understanding of complex phenomena encountered in science and engineering. An argument based on set theory is used to analyze three examples that illustrate the shortcomings of the reductionist approach. Using these cases as motivational points, a holistic approach to understand complex phenomena is proposed, whereby the human brain acts as a template to do so. Recognizing the need to maintain the transparency of the analysis provided by reductionism, a promising computational approach is offered by which the brain is used as a template for understanding complex phenomena. Some of the details of implementing this approach are also addressed.
