In this paper,we propose a decentralized algorithm to solve the low-rank matrix completion problem and analyze its privacy-preserving property.Suppose that we want to recover a low-rank matrix D=[D1,D2,・・・,DL]from a s...In this paper,we propose a decentralized algorithm to solve the low-rank matrix completion problem and analyze its privacy-preserving property.Suppose that we want to recover a low-rank matrix D=[D1,D2,・・・,DL]from a subset of its entries.In a network composed of L agents,each agent i observes some entries of Di.We factorize the unknown matrix D as the product of a public matrix X which is common to all agents and a private matrix Y=[Y1,Y2,・・・,YL]of which Yi is held by agent i only.Each agent i updates Yi and its local estimate of X,denoted by X(i),in an alternating manner.Through exchanging information with neighbors,all the agents move toward a consensus on the estimates X(i).Once the consensus is(nearly)reached throughout the network,each agent i recovers Di=X(i)Yi,thus D is recovered.In this progress,communication through the network may disclose sensitive information about the data matrices Di to a malicious agent.We prove that in the proposed algorithm,D-LMaFit,if the network topology is well designed,the malicious agent is unable to reconstruct the sensitive information from others.展开更多
With the advancement of the“carbon peaking”and“carbon neutrality”objectives,concerns regarding carbon emissions in energy system dispatching have attracted much attention.The integration of electricity and gas sys...With the advancement of the“carbon peaking”and“carbon neutrality”objectives,concerns regarding carbon emissions in energy system dispatching have attracted much attention.The integration of electricity and gas systems(IEGS),with carbon capture power plants and power-to-gas(CCPP-P2G)facilities can facilitate flexible dispatching of multiple energy sources.This integration is conducive to the low-carbon and economically efficient operation of IEGS.Current research did not comprehensively consider the emission mitigation responsibility of the source-demand side.A bi-layer decentralized lowcarbon optimal dispatching model on both source and demand sides is proposed in this paper.On the demand side,the carbon emissions and carbon caps are allocated based on marginal carbon intensity.Then a low-carbon demand response mechanism considering step-based carbon price is established to explore the low-carbon potentials of electrical and natural gas loads.An optimal dispatching model,incorporating carbon emission constraints,is formulated on the source side through the analysis of the operational characteristics of CCPP-P2G.Furthermore,the decentralized Alternating Direction Method of Multipliers(ADMM)algorithm is employed to solve the bi-layer optimal model while protecting the data privacy of both IEGS operators and users.Case studies validate the environmental and economic benefits of the proposed low-carbon dispatching model.展开更多
文摘In this paper,we propose a decentralized algorithm to solve the low-rank matrix completion problem and analyze its privacy-preserving property.Suppose that we want to recover a low-rank matrix D=[D1,D2,・・・,DL]from a subset of its entries.In a network composed of L agents,each agent i observes some entries of Di.We factorize the unknown matrix D as the product of a public matrix X which is common to all agents and a private matrix Y=[Y1,Y2,・・・,YL]of which Yi is held by agent i only.Each agent i updates Yi and its local estimate of X,denoted by X(i),in an alternating manner.Through exchanging information with neighbors,all the agents move toward a consensus on the estimates X(i).Once the consensus is(nearly)reached throughout the network,each agent i recovers Di=X(i)Yi,thus D is recovered.In this progress,communication through the network may disclose sensitive information about the data matrices Di to a malicious agent.We prove that in the proposed algorithm,D-LMaFit,if the network topology is well designed,the malicious agent is unable to reconstruct the sensitive information from others.
基金supported by the National Natural Science Foundation of China under grant 52177073.
文摘With the advancement of the“carbon peaking”and“carbon neutrality”objectives,concerns regarding carbon emissions in energy system dispatching have attracted much attention.The integration of electricity and gas systems(IEGS),with carbon capture power plants and power-to-gas(CCPP-P2G)facilities can facilitate flexible dispatching of multiple energy sources.This integration is conducive to the low-carbon and economically efficient operation of IEGS.Current research did not comprehensively consider the emission mitigation responsibility of the source-demand side.A bi-layer decentralized lowcarbon optimal dispatching model on both source and demand sides is proposed in this paper.On the demand side,the carbon emissions and carbon caps are allocated based on marginal carbon intensity.Then a low-carbon demand response mechanism considering step-based carbon price is established to explore the low-carbon potentials of electrical and natural gas loads.An optimal dispatching model,incorporating carbon emission constraints,is formulated on the source side through the analysis of the operational characteristics of CCPP-P2G.Furthermore,the decentralized Alternating Direction Method of Multipliers(ADMM)algorithm is employed to solve the bi-layer optimal model while protecting the data privacy of both IEGS operators and users.Case studies validate the environmental and economic benefits of the proposed low-carbon dispatching model.
