The coordinated optimization problem of the electricity-gas-heat integrated energy system(IES)has the characteristics of strong coupling,non-convexity,and nonlinearity.The centralized optimization method has a high co...The coordinated optimization problem of the electricity-gas-heat integrated energy system(IES)has the characteristics of strong coupling,non-convexity,and nonlinearity.The centralized optimization method has a high cost of communication and complex modeling.Meanwhile,the traditional numerical iterative solution cannot deal with uncertainty and solution efficiency,which is difficult to apply online.For the coordinated optimization problem of the electricity-gas-heat IES in this study,we constructed a model for the distributed IES with a dynamic distribution factor and transformed the centralized optimization problem into a distributed optimization problem in the multi-agent reinforcement learning environment using multi-agent deep deterministic policy gradient.Introducing the dynamic distribution factor allows the system to consider the impact of changes in real-time supply and demand on system optimization,dynamically coordinating different energy sources for complementary utilization and effectively improving the system economy.Compared with centralized optimization,the distributed model with multiple decision centers can achieve similar results while easing the pressure on system communication.The proposed method considers the dual uncertainty of renewable energy and load in the training.Compared with the traditional iterative solution method,it can better cope with uncertainty and realize real-time decision making of the system,which is conducive to the online application.Finally,we verify the effectiveness of the proposed method using an example of an IES coupled with three energy hub agents.展开更多
With the increasing development of smart grid,multi-party cooperative computation between several entities has become a typical characteristic of modern energy systems.Traditionally,data exchange among parties is inev...With the increasing development of smart grid,multi-party cooperative computation between several entities has become a typical characteristic of modern energy systems.Traditionally,data exchange among parties is inevitable,rendering how to complete multi-party collaborative optimization without exposing any private information a critical issue.This paper proposes a fully privacy-preserving distributed optimization framework based on secure multi-party computation(SMPC)with secret sharing protocols.The framework decomposes the collaborative optimization problem into a master problem and several subproblems.The process of solving the master problem is executed in the SMPC framework via the secret sharing protocols among agents.The relationships of agents are completely equal,and there is no privileged agent or any third party.The process of solving subproblems is conducted by agents individually.Compared to the traditional distributed optimization framework,the proposed SMPC-based framework can fully preserve individual private information.Exchanged data among agents are encrypted and no private information disclosure is assured.Furthermore,the framework maintains a limited and acceptable increase in computational costs while guaranteeing opti-mality.Case studies are conducted on test systems of different scales to demonstrate the principle of secret sharing and verify the feasibility and scalability of the proposed methodology.展开更多
We study distributed optimization problems over a directed network,where nodes aim to minimize the sum of local objective functions via directed communications with neighbors.Many algorithms are designed to solve it f...We study distributed optimization problems over a directed network,where nodes aim to minimize the sum of local objective functions via directed communications with neighbors.Many algorithms are designed to solve it for synchronized or randomly activated implementation,which may create deadlocks in practice.In sharp contrast,we propose a fully asynchronous push-pull gradient(APPG) algorithm,where each node updates without waiting for any other node by using possibly delayed information from neighbors.Then,we construct two novel augmented networks to analyze asynchrony and delays,and quantify its convergence rate from the worst-case point of view.Particularly,all nodes of APPG converge to the same optimal solution at a linear rate of O(λ^(k)) if local functions have Lipschitz-continuous gradients and their sum satisfies the Polyak-?ojasiewicz condition(convexity is not required),where λ ∈(0,1) is explicitly given and the virtual counter k increases by one when any node updates.Finally,the advantage of APPG over the synchronous counterpart and its linear speedup efficiency are numerically validated via a logistic regression problem.展开更多
This paper addresses the distributed optimization problem of discrete-time multiagent systems with nonconvex control input constraints and switching topologies.We introduce a novel distributed optimization algorithm w...This paper addresses the distributed optimization problem of discrete-time multiagent systems with nonconvex control input constraints and switching topologies.We introduce a novel distributed optimization algorithm with a switching mechanism to guarantee that all agents eventually converge to an optimal solution point,while their control inputs are constrained in their own nonconvex region.It is worth noting that the mechanism is performed to tackle the coexistence of the nonconvex constraint operator and the optimization gradient term.Based on the dynamic transformation technique,the original nonlinear dynamic system is transformed into an equivalent one with a nonlinear error term.By utilizing the nonnegative matrix theory,it is shown that the optimization problem can be solved when the union of switching communication graphs is jointly strongly connected.Finally,a numerical simulation example is used to demonstrate the acquired theoretical results.展开更多
In this paper,the problem of online distributed optimization subject to a convex set is studied via a network of agents.Each agent only has access to a noisy gradient of its own objective function,and can communicate ...In this paper,the problem of online distributed optimization subject to a convex set is studied via a network of agents.Each agent only has access to a noisy gradient of its own objective function,and can communicate with its neighbors via a network.To handle this problem,an online distributed stochastic mirror descent algorithm is proposed.Existing works on online distributed algorithms involving stochastic gradients only provide the expectation bounds of the regrets.Different from them,we study the high probability bound of the regrets,i.e.,the sublinear bound of the regret is characterized by the natural logarithm of the failure probability's inverse.Under mild assumptions on the graph connectivity,we prove that the dynamic regret grows sublinearly with a high probability if the deviation in the minimizer sequence is sublinear with the square root of the time horizon.Finally,a simulation is provided to demonstrate the effectiveness of our theoretical results.展开更多
This paper focuses on the online distributed optimization problem based on multi-agent systems. In this problem, each agent can only access its own cost function and a convex set, and can only exchange local state inf...This paper focuses on the online distributed optimization problem based on multi-agent systems. In this problem, each agent can only access its own cost function and a convex set, and can only exchange local state information with its current neighbors through a time-varying digraph. In addition, the agents do not have access to the information about the current cost functions until decisions are made. Different from most existing works on online distributed optimization, here we consider the case where the cost functions are strongly pseudoconvex and real gradients of the cost functions are not available. To handle this problem, a random gradient-free online distributed algorithm involving the multi-point gradient estimator is proposed. Of particular interest is that under the proposed algorithm, each agent only uses the estimation information of gradients instead of the real gradient information to make decisions. The dynamic regret is employed to measure the proposed algorithm. We prove that if the cumulative deviation of the minimizer sequence grows within a certain rate, then the expectation of dynamic regret increases sublinearly. Finally, a simulation example is given to corroborate the validity of our results.展开更多
A continuous⁃time distributed optimization was researched for second⁃order heterogeneous multi⁃agent systems.The aim of this study is to keep the velocities of all agents the same and make the velocities converge to t...A continuous⁃time distributed optimization was researched for second⁃order heterogeneous multi⁃agent systems.The aim of this study is to keep the velocities of all agents the same and make the velocities converge to the optimal value to minimize the sum of local cost functions.First,an effective distributed controller which only uses local information was designed.Then,the stability and optimization of the systems were verified.Finally,a simulation case was used to illustrate the analytical results.展开更多
Dear Editor,This letter addresses distributed optimization for resource allocation problems with time-varying objective functions and time-varying constraints.Inspired by the distributed average tracking(DAT)approach,...Dear Editor,This letter addresses distributed optimization for resource allocation problems with time-varying objective functions and time-varying constraints.Inspired by the distributed average tracking(DAT)approach,a distributed control protocol is proposed for optimal resource allocation.The convergence to a time-varying optimal solution within a predefined time is proved.Two numerical examples are given to illustrate the effectiveness of the proposed approach.展开更多
Considering the complexity of plant-wide optimization for large-scale industries, a distributed optimization framework to solve the profit optimization problem in ethylene whole process is proposed. To tackle the dela...Considering the complexity of plant-wide optimization for large-scale industries, a distributed optimization framework to solve the profit optimization problem in ethylene whole process is proposed. To tackle the delays arising from the residence time for materials passing through production units during the process with guaranteed constraint satisfaction, an asynchronous distributed parameter projection algorithm with gradient tracking method is introduced. Besides, the heavy ball momentum and Nesterov momentum are incorporated into the proposed algorithm in order to achieve double acceleration properties. The experimental results show that the proposed asynchronous algorithm can achieve a faster convergence compared with the synchronous algorithm.展开更多
This paper focuses on solving the distributed optimization problem with binary-valued intermittent measurements of local objective functions.In this paper,a binary-valued measurement represents whether the measured va...This paper focuses on solving the distributed optimization problem with binary-valued intermittent measurements of local objective functions.In this paper,a binary-valued measurement represents whether the measured value is smaller than a fixed threshold.Meanwhile,the“intermittent”scenario arises when there is a non-zero probability of not detecting each local function value during the measuring process.Using this kind of coarse measurement,the authors propose a discrete-time stochastic extremum seeking-based algorithm for distributed optimization over a directed graph.As is well-known,many existing distributed optimization algorithms require a doubly-stochastic weight matrix to ensure the average consensus of agents.However,in practical engineering,achieving doublestochasticity,especially for directed graphs,is not always feasible or desirable.To overcome this limitation,the authors design a row-stochastic matrix and a column-stochastic matrix as weight matrices in the proposed algorithm instead of relying on doubly-stochasticity.Under some mild conditions,the authors rigorously prove that agents can reach the average consensus and ultimately find the optimal solution.Finally,the authors provide a numerical example to illustrate the effectiveness of the algorithm.展开更多
In this paper,we consider the distributed online optimization problem on a time-varying network,where each agent on the network has its own time-varying objective function and the goal is to minimize the overall loss ...In this paper,we consider the distributed online optimization problem on a time-varying network,where each agent on the network has its own time-varying objective function and the goal is to minimize the overall loss accumulated.Moreover,we focus on distributed algorithms which do not use gradient information and projection operators to improve the applicability and computational efficiency.By introducing the deterministic differences and the randomized differences to substitute the gradient information of the objective functions and removing the projection operator in the traditional algorithms,we design two kinds of gradient-free distributed online optimization algorithms without projection step,which can economize considerable computational resources as well as has less limitations on the applicability.We prove that both of two algorithms achieves consensus of the estimates and regrets of\(O\left(\log(T)\right)\)for local strongly convex objective,respectively.Finally,a simulation example is provided to verify the theoretical results.展开更多
This paper investigates a class of constrained distributed zeroth-order optimization(ZOO) problems over timevarying unbalanced graphs while ensuring privacy preservation among individual agents. Not taking into accoun...This paper investigates a class of constrained distributed zeroth-order optimization(ZOO) problems over timevarying unbalanced graphs while ensuring privacy preservation among individual agents. Not taking into account recent progress and addressing these concerns separately, there remains a lack of solutions offering theoretical guarantees for both privacy protection and constrained ZOO over time-varying unbalanced graphs.We hereby propose a novel algorithm, termed the differential privacy(DP) distributed push-sum based zeroth-order constrained optimization algorithm(DP-ZOCOA). Operating over time-varying unbalanced graphs, DP-ZOCOA obviates the need for supplemental suboptimization problem computations, thereby reducing overhead in comparison to distributed primary-dual methods. DP-ZOCOA is specifically tailored to tackle constrained ZOO problems over time-varying unbalanced graphs,offering a guarantee of convergence to the optimal solution while robustly preserving privacy. Moreover, we provide rigorous proofs of convergence and privacy for DP-ZOCOA, underscoring its efficacy in attaining optimal convergence without constraints. To enhance its applicability, we incorporate DP-ZOCOA into the federated learning framework and formulate a decentralized zeroth-order constrained federated learning algorithm(ZOCOA-FL) to address challenges stemming from the timevarying imbalance of communication topology. Finally, the performance and effectiveness of the proposed algorithms are thoroughly evaluated through simulations on distributed least squares(DLS) and decentralized federated learning(DFL) tasks.展开更多
In this paper,we consider distributed convex optimization problems on multi-agent networks.We develop and analyze the distributed gradient method which allows each agent to compute its dynamic stepsize by utilizing th...In this paper,we consider distributed convex optimization problems on multi-agent networks.We develop and analyze the distributed gradient method which allows each agent to compute its dynamic stepsize by utilizing the time-varying estimate of the local function value at the global optimal solution.Our approach can be applied to both synchronous and asynchronous communication protocols.Specifically,we propose the distributed subgradient with uncoordinated dynamic stepsizes(DS-UD)algorithm for synchronous protocol and the AsynDGD algorithm for asynchronous protocol.Theoretical analysis shows that the proposed algorithms guarantee that all agents reach a consensus on the solution to the multi-agent optimization problem.Moreover,the proposed approach with dynamic stepsizes eliminates the requirement of diminishing stepsize in existing works.Numerical examples of distributed estimation in sensor networks are provided to illustrate the effectiveness of the proposed approach.展开更多
This paper considers distributed stochastic optimization,in which a number of agents cooperate to optimize a global objective function through local computations and information exchanges with neighbors over a network...This paper considers distributed stochastic optimization,in which a number of agents cooperate to optimize a global objective function through local computations and information exchanges with neighbors over a network.Stochastic optimization problems are usually tackled by variants of projected stochastic gradient descent.However,projecting a point onto a feasible set is often expensive.The Frank-Wolfe(FW)method has well-documented merits in handling convex constraints,but existing stochastic FW algorithms are basically developed for centralized settings.In this context,the present work puts forth a distributed stochastic Frank-Wolfe solver,by judiciously combining Nesterov's momentum and gradient tracking techniques for stochastic convex and nonconvex optimization over networks.It is shown that the convergence rate of the proposed algorithm is O(k^(-1/2))for convex optimization,and O(1/log_(2)(k))for nonconvex optimization.The efficacy of the algorithm is demonstrated by numerical simulations against a number of competing alternatives.展开更多
The heating,ventilation,and air-conditioning(HVAC)systems account for about half of the building energy consumption.The optimization methodology access to optimal control strategies of chiller plant has always been of...The heating,ventilation,and air-conditioning(HVAC)systems account for about half of the building energy consumption.The optimization methodology access to optimal control strategies of chiller plant has always been of great concern as it significantly contributes to the energy use of the whole HVAC system.Given that conventional centralized optimization methods relying on a central operator may suffer from dimensionality and a tremendous calculation burden,and show poorer flexibility when solving complex optimization issues,in this paper,a novel distributed optimization approach is presented for chiller plant control.In the proposed distributed control scheme,both trade-offs of coupled subsystems and optimal allocation among devices of the same subsystem are considered by developing a double-layer optimization structure.Non-cooperative game is used to mathematically formulate the interaction between controlled components as well as to divide the initial system-scale nonlinear optimization problem into local-scale ones.To solve these tasks,strategy updating mechanisms(PSO and IPM)are utilized.In this way,the approximate global optimal controlled variables of devices in the chiller plant can be obtained in a distributed and local-knowledge-enabled way without neither global information nor the central workstation.Furthermore,the existence and effectiveness of the proposed distributed scheme were verified by simulation case studies.Simulation results indicate that,by using the proposed distributed optimization scheme,a significant energy saving on a typical summer day can be obtained(1809.47 kW·h).The deviation from the central optimal solution is 3.83%.展开更多
This paper studies the distributed optimization problem when the objective functions might be nondifferentiable and subject to heterogeneous set constraints.Unlike existing subgradient methods,the authors focus on the...This paper studies the distributed optimization problem when the objective functions might be nondifferentiable and subject to heterogeneous set constraints.Unlike existing subgradient methods,the authors focus on the case when the exact subgradients of the local objective functions can not be accessed by the agents.To solve this problem,the authors propose a projected primaldual dynamics using only the objective function’s approximate subgradients.The authors first prove that the formulated optimization problem can generally be solved with an error depending upon the accuracy of the available subgradients.Then,the authors show the exact solvability of this distributed optimization problem when the accumulated approximation error of inexact subgradients is not too large.After that,the authors also give a novel componentwise normalized variant to improve the transient behavior of the convergent sequence.The effectiveness of the proposed algorithms is verified by a numerical example.展开更多
In this paper,the distributed optimization problem is investigated for a class of general nonlinear model-free multi-agent systems.The dynamical model of each agent is unknown and only the input/output data are availa...In this paper,the distributed optimization problem is investigated for a class of general nonlinear model-free multi-agent systems.The dynamical model of each agent is unknown and only the input/output data are available.A model-free adaptive control method is employed,by which the original unknown nonlinear system is equivalently converted into a dynamic linearized model.An event-triggered consensus scheme is developed to guarantee that the consensus error of the outputs of all agents is convergent.Then,by means of the distributed gradient descent method,a novel event-triggered model-free adaptive distributed optimization algorithm is put forward.Sufficient conditions are established to ensure the consensus and optimality of the addressed system.Finally,simulation results are provided to validate the effectiveness of the proposed approach.展开更多
In this paper,we develop a distributed solver for a group of strict(non-strict)linear matrix inequalities over a multi-agent network,where each agent only knows one inequality,and all agents co-operate to reach a cons...In this paper,we develop a distributed solver for a group of strict(non-strict)linear matrix inequalities over a multi-agent network,where each agent only knows one inequality,and all agents co-operate to reach a consensus solution in the intersection of all the feasible regions.The formulation is transformed into a distributed optimization problem by introducing slack variables and consensus constraints.Then,by the primal–dual methods,a distributed algorithm is proposed with the help of projection operators and derivative feedback.Finally,the convergence of the algorithm is analyzed,followed by illustrative simulations.展开更多
In this paper,the optimization problem subject to N nonidentical closed convex set constraints is studied.The aim is to design a corresponding distributed optimization algorithm over the fixed unbalanced graph to solv...In this paper,the optimization problem subject to N nonidentical closed convex set constraints is studied.The aim is to design a corresponding distributed optimization algorithm over the fixed unbalanced graph to solve the considered problem.To this end,with the push-sum framework improved,the distributed optimization algorithm is newly designed,and its strict convergence analysis is given under the assumption that the involved graph is strongly connected.Finally,simulation results support the good performance of the proposed algorithm.展开更多
The state-based potential game is discussed and a game-based approach is proposed for distributed optimization problem in this paper.A continuous-time model is employed to design the state dynamics and learning algori...The state-based potential game is discussed and a game-based approach is proposed for distributed optimization problem in this paper.A continuous-time model is employed to design the state dynamics and learning algorithms of the state-based potential game with Lagrangian multipliers as the states.It is shown that the stationary state Nash equilibrium of the designed game contains the optimal solution of the optimization problem.Moreover,the convergence and stability of the learning algorithms are obtained for both undirected and directed communication graph.Additionally,the application to plug-in electric vehicle management is also discussed.展开更多
基金supported by The National Key R&D Program of China(2020YFB0905900):Research on artificial intelligence application of power internet of things.
文摘The coordinated optimization problem of the electricity-gas-heat integrated energy system(IES)has the characteristics of strong coupling,non-convexity,and nonlinearity.The centralized optimization method has a high cost of communication and complex modeling.Meanwhile,the traditional numerical iterative solution cannot deal with uncertainty and solution efficiency,which is difficult to apply online.For the coordinated optimization problem of the electricity-gas-heat IES in this study,we constructed a model for the distributed IES with a dynamic distribution factor and transformed the centralized optimization problem into a distributed optimization problem in the multi-agent reinforcement learning environment using multi-agent deep deterministic policy gradient.Introducing the dynamic distribution factor allows the system to consider the impact of changes in real-time supply and demand on system optimization,dynamically coordinating different energy sources for complementary utilization and effectively improving the system economy.Compared with centralized optimization,the distributed model with multiple decision centers can achieve similar results while easing the pressure on system communication.The proposed method considers the dual uncertainty of renewable energy and load in the training.Compared with the traditional iterative solution method,it can better cope with uncertainty and realize real-time decision making of the system,which is conducive to the online application.Finally,we verify the effectiveness of the proposed method using an example of an IES coupled with three energy hub agents.
基金supported in part by the National Key Research and Development Program of China 2020YFB2104500.
文摘With the increasing development of smart grid,multi-party cooperative computation between several entities has become a typical characteristic of modern energy systems.Traditionally,data exchange among parties is inevitable,rendering how to complete multi-party collaborative optimization without exposing any private information a critical issue.This paper proposes a fully privacy-preserving distributed optimization framework based on secure multi-party computation(SMPC)with secret sharing protocols.The framework decomposes the collaborative optimization problem into a master problem and several subproblems.The process of solving the master problem is executed in the SMPC framework via the secret sharing protocols among agents.The relationships of agents are completely equal,and there is no privileged agent or any third party.The process of solving subproblems is conducted by agents individually.Compared to the traditional distributed optimization framework,the proposed SMPC-based framework can fully preserve individual private information.Exchanged data among agents are encrypted and no private information disclosure is assured.Furthermore,the framework maintains a limited and acceptable increase in computational costs while guaranteeing opti-mality.Case studies are conducted on test systems of different scales to demonstrate the principle of secret sharing and verify the feasibility and scalability of the proposed methodology.
基金Supported by National Natural Science Foundation of China(62033006,62203254)。
文摘We study distributed optimization problems over a directed network,where nodes aim to minimize the sum of local objective functions via directed communications with neighbors.Many algorithms are designed to solve it for synchronized or randomly activated implementation,which may create deadlocks in practice.In sharp contrast,we propose a fully asynchronous push-pull gradient(APPG) algorithm,where each node updates without waiting for any other node by using possibly delayed information from neighbors.Then,we construct two novel augmented networks to analyze asynchrony and delays,and quantify its convergence rate from the worst-case point of view.Particularly,all nodes of APPG converge to the same optimal solution at a linear rate of O(λ^(k)) if local functions have Lipschitz-continuous gradients and their sum satisfies the Polyak-?ojasiewicz condition(convexity is not required),where λ ∈(0,1) is explicitly given and the virtual counter k increases by one when any node updates.Finally,the advantage of APPG over the synchronous counterpart and its linear speedup efficiency are numerically validated via a logistic regression problem.
基金Project supported by the National Engineering Research Center of Rail Transportation Operation and Control System,Beijing Jiaotong University(Grant No.NERC2019K002)。
文摘This paper addresses the distributed optimization problem of discrete-time multiagent systems with nonconvex control input constraints and switching topologies.We introduce a novel distributed optimization algorithm with a switching mechanism to guarantee that all agents eventually converge to an optimal solution point,while their control inputs are constrained in their own nonconvex region.It is worth noting that the mechanism is performed to tackle the coexistence of the nonconvex constraint operator and the optimization gradient term.Based on the dynamic transformation technique,the original nonlinear dynamic system is transformed into an equivalent one with a nonlinear error term.By utilizing the nonnegative matrix theory,it is shown that the optimization problem can be solved when the union of switching communication graphs is jointly strongly connected.Finally,a numerical simulation example is used to demonstrate the acquired theoretical results.
文摘In this paper,the problem of online distributed optimization subject to a convex set is studied via a network of agents.Each agent only has access to a noisy gradient of its own objective function,and can communicate with its neighbors via a network.To handle this problem,an online distributed stochastic mirror descent algorithm is proposed.Existing works on online distributed algorithms involving stochastic gradients only provide the expectation bounds of the regrets.Different from them,we study the high probability bound of the regrets,i.e.,the sublinear bound of the regret is characterized by the natural logarithm of the failure probability's inverse.Under mild assumptions on the graph connectivity,we prove that the dynamic regret grows sublinearly with a high probability if the deviation in the minimizer sequence is sublinear with the square root of the time horizon.Finally,a simulation is provided to demonstrate the effectiveness of our theoretical results.
基金supported by the National Natural Science Foundation of China(Nos.62103169,51875380)the China Postdoctoral Science Foundation(No.2021M691313).
文摘This paper focuses on the online distributed optimization problem based on multi-agent systems. In this problem, each agent can only access its own cost function and a convex set, and can only exchange local state information with its current neighbors through a time-varying digraph. In addition, the agents do not have access to the information about the current cost functions until decisions are made. Different from most existing works on online distributed optimization, here we consider the case where the cost functions are strongly pseudoconvex and real gradients of the cost functions are not available. To handle this problem, a random gradient-free online distributed algorithm involving the multi-point gradient estimator is proposed. Of particular interest is that under the proposed algorithm, each agent only uses the estimation information of gradients instead of the real gradient information to make decisions. The dynamic regret is employed to measure the proposed algorithm. We prove that if the cumulative deviation of the minimizer sequence grows within a certain rate, then the expectation of dynamic regret increases sublinearly. Finally, a simulation example is given to corroborate the validity of our results.
基金Sponsored by the National Natural Science Foundation of China(Grant Nos.61573199 and 61571441)。
文摘A continuous⁃time distributed optimization was researched for second⁃order heterogeneous multi⁃agent systems.The aim of this study is to keep the velocities of all agents the same and make the velocities converge to the optimal value to minimize the sum of local cost functions.First,an effective distributed controller which only uses local information was designed.Then,the stability and optimization of the systems were verified.Finally,a simulation case was used to illustrate the analytical results.
基金supported by National Key Research and Development Program of China(2024YFE0214000)National Natural Science Foundation of China(62173308)+3 种基金Natural Science Foundation of Zhejiang Province of China(LRG25F030002)Zhejiang Province Leading Geese Plan(2025C01056)Jinhua Science and Technology Project(2022-1-042)Natural Science Foundation of Jiangsu Province(BK20240009).
文摘Dear Editor,This letter addresses distributed optimization for resource allocation problems with time-varying objective functions and time-varying constraints.Inspired by the distributed average tracking(DAT)approach,a distributed control protocol is proposed for optimal resource allocation.The convergence to a time-varying optimal solution within a predefined time is proved.Two numerical examples are given to illustrate the effectiveness of the proposed approach.
基金supported by National Key Research and Development Program of China(2022YFB3305900)National Natural Science Foundation of China(62394343,62394345)+1 种基金Major Science and Technology Projects of Longmen Laboratory(NO.LMZDXM202206)Shanghai Rising-Star Program under Grant 24QA2706100.
文摘Considering the complexity of plant-wide optimization for large-scale industries, a distributed optimization framework to solve the profit optimization problem in ethylene whole process is proposed. To tackle the delays arising from the residence time for materials passing through production units during the process with guaranteed constraint satisfaction, an asynchronous distributed parameter projection algorithm with gradient tracking method is introduced. Besides, the heavy ball momentum and Nesterov momentum are incorporated into the proposed algorithm in order to achieve double acceleration properties. The experimental results show that the proposed asynchronous algorithm can achieve a faster convergence compared with the synchronous algorithm.
基金supported by the National Natural Science Foundation of China under Grant No.62473272the Natural Science Foundation of Sichuan Province,China under Grant No.2024NSFSC0437。
文摘This paper focuses on solving the distributed optimization problem with binary-valued intermittent measurements of local objective functions.In this paper,a binary-valued measurement represents whether the measured value is smaller than a fixed threshold.Meanwhile,the“intermittent”scenario arises when there is a non-zero probability of not detecting each local function value during the measuring process.Using this kind of coarse measurement,the authors propose a discrete-time stochastic extremum seeking-based algorithm for distributed optimization over a directed graph.As is well-known,many existing distributed optimization algorithms require a doubly-stochastic weight matrix to ensure the average consensus of agents.However,in practical engineering,achieving doublestochasticity,especially for directed graphs,is not always feasible or desirable.To overcome this limitation,the authors design a row-stochastic matrix and a column-stochastic matrix as weight matrices in the proposed algorithm instead of relying on doubly-stochasticity.Under some mild conditions,the authors rigorously prove that agents can reach the average consensus and ultimately find the optimal solution.Finally,the authors provide a numerical example to illustrate the effectiveness of the algorithm.
文摘In this paper,we consider the distributed online optimization problem on a time-varying network,where each agent on the network has its own time-varying objective function and the goal is to minimize the overall loss accumulated.Moreover,we focus on distributed algorithms which do not use gradient information and projection operators to improve the applicability and computational efficiency.By introducing the deterministic differences and the randomized differences to substitute the gradient information of the objective functions and removing the projection operator in the traditional algorithms,we design two kinds of gradient-free distributed online optimization algorithms without projection step,which can economize considerable computational resources as well as has less limitations on the applicability.We prove that both of two algorithms achieves consensus of the estimates and regrets of\(O\left(\log(T)\right)\)for local strongly convex objective,respectively.Finally,a simulation example is provided to verify the theoretical results.
基金supported in part by the National Key Research and Development Program of China(2022ZD0120001)the National Natural Science Foundation of China(62233004,62273090,62073076)the Jiangsu Provincial Scientific Research Center of Applied Mathematics(BK20233002)
文摘This paper investigates a class of constrained distributed zeroth-order optimization(ZOO) problems over timevarying unbalanced graphs while ensuring privacy preservation among individual agents. Not taking into account recent progress and addressing these concerns separately, there remains a lack of solutions offering theoretical guarantees for both privacy protection and constrained ZOO over time-varying unbalanced graphs.We hereby propose a novel algorithm, termed the differential privacy(DP) distributed push-sum based zeroth-order constrained optimization algorithm(DP-ZOCOA). Operating over time-varying unbalanced graphs, DP-ZOCOA obviates the need for supplemental suboptimization problem computations, thereby reducing overhead in comparison to distributed primary-dual methods. DP-ZOCOA is specifically tailored to tackle constrained ZOO problems over time-varying unbalanced graphs,offering a guarantee of convergence to the optimal solution while robustly preserving privacy. Moreover, we provide rigorous proofs of convergence and privacy for DP-ZOCOA, underscoring its efficacy in attaining optimal convergence without constraints. To enhance its applicability, we incorporate DP-ZOCOA into the federated learning framework and formulate a decentralized zeroth-order constrained federated learning algorithm(ZOCOA-FL) to address challenges stemming from the timevarying imbalance of communication topology. Finally, the performance and effectiveness of the proposed algorithms are thoroughly evaluated through simulations on distributed least squares(DLS) and decentralized federated learning(DFL) tasks.
基金supported by the Key Research and Development Project in Guangdong Province(2020B0101050001)the National Science Foundation of China(61973214,61590924,61963030)the Natural Science Foundation of Shanghai(19ZR1476200)。
文摘In this paper,we consider distributed convex optimization problems on multi-agent networks.We develop and analyze the distributed gradient method which allows each agent to compute its dynamic stepsize by utilizing the time-varying estimate of the local function value at the global optimal solution.Our approach can be applied to both synchronous and asynchronous communication protocols.Specifically,we propose the distributed subgradient with uncoordinated dynamic stepsizes(DS-UD)algorithm for synchronous protocol and the AsynDGD algorithm for asynchronous protocol.Theoretical analysis shows that the proposed algorithms guarantee that all agents reach a consensus on the solution to the multi-agent optimization problem.Moreover,the proposed approach with dynamic stepsizes eliminates the requirement of diminishing stepsize in existing works.Numerical examples of distributed estimation in sensor networks are provided to illustrate the effectiveness of the proposed approach.
基金supported in part by the National Key R&D Program of China(2021YFB1714800)the National Natural Science Foundation of China(62222303,62073035,62173034,61925303,62088101,61873033)+1 种基金the CAAI-Huawei MindSpore Open Fundthe Chongqing Natural Science Foundation(2021ZX4100027)。
文摘This paper considers distributed stochastic optimization,in which a number of agents cooperate to optimize a global objective function through local computations and information exchanges with neighbors over a network.Stochastic optimization problems are usually tackled by variants of projected stochastic gradient descent.However,projecting a point onto a feasible set is often expensive.The Frank-Wolfe(FW)method has well-documented merits in handling convex constraints,but existing stochastic FW algorithms are basically developed for centralized settings.In this context,the present work puts forth a distributed stochastic Frank-Wolfe solver,by judiciously combining Nesterov's momentum and gradient tracking techniques for stochastic convex and nonconvex optimization over networks.It is shown that the convergence rate of the proposed algorithm is O(k^(-1/2))for convex optimization,and O(1/log_(2)(k))for nonconvex optimization.The efficacy of the algorithm is demonstrated by numerical simulations against a number of competing alternatives.
基金supported by the National Natural Science Foundation of China(No.51978481)support provided by China Scholarship Council(No.202006260140)。
文摘The heating,ventilation,and air-conditioning(HVAC)systems account for about half of the building energy consumption.The optimization methodology access to optimal control strategies of chiller plant has always been of great concern as it significantly contributes to the energy use of the whole HVAC system.Given that conventional centralized optimization methods relying on a central operator may suffer from dimensionality and a tremendous calculation burden,and show poorer flexibility when solving complex optimization issues,in this paper,a novel distributed optimization approach is presented for chiller plant control.In the proposed distributed control scheme,both trade-offs of coupled subsystems and optimal allocation among devices of the same subsystem are considered by developing a double-layer optimization structure.Non-cooperative game is used to mathematically formulate the interaction between controlled components as well as to divide the initial system-scale nonlinear optimization problem into local-scale ones.To solve these tasks,strategy updating mechanisms(PSO and IPM)are utilized.In this way,the approximate global optimal controlled variables of devices in the chiller plant can be obtained in a distributed and local-knowledge-enabled way without neither global information nor the central workstation.Furthermore,the existence and effectiveness of the proposed distributed scheme were verified by simulation case studies.Simulation results indicate that,by using the proposed distributed optimization scheme,a significant energy saving on a typical summer day can be obtained(1809.47 kW·h).The deviation from the central optimal solution is 3.83%.
基金supported by the National Natural Science Foundation of China under Grant No.61973043。
文摘This paper studies the distributed optimization problem when the objective functions might be nondifferentiable and subject to heterogeneous set constraints.Unlike existing subgradient methods,the authors focus on the case when the exact subgradients of the local objective functions can not be accessed by the agents.To solve this problem,the authors propose a projected primaldual dynamics using only the objective function’s approximate subgradients.The authors first prove that the formulated optimization problem can generally be solved with an error depending upon the accuracy of the available subgradients.Then,the authors show the exact solvability of this distributed optimization problem when the accumulated approximation error of inexact subgradients is not too large.After that,the authors also give a novel componentwise normalized variant to improve the transient behavior of the convergent sequence.The effectiveness of the proposed algorithms is verified by a numerical example.
基金Project supported by the National Natural Science Foundation of China(No.62003213)。
文摘In this paper,the distributed optimization problem is investigated for a class of general nonlinear model-free multi-agent systems.The dynamical model of each agent is unknown and only the input/output data are available.A model-free adaptive control method is employed,by which the original unknown nonlinear system is equivalently converted into a dynamic linearized model.An event-triggered consensus scheme is developed to guarantee that the consensus error of the outputs of all agents is convergent.Then,by means of the distributed gradient descent method,a novel event-triggered model-free adaptive distributed optimization algorithm is put forward.Sufficient conditions are established to ensure the consensus and optimality of the addressed system.Finally,simulation results are provided to validate the effectiveness of the proposed approach.
基金This work was supported by the Shanghai Municipal Science and Technology Major Project(No.2021SHZDZX0100)the National Natural Science Foundation of China(Nos.61733018,62073035)。
文摘In this paper,we develop a distributed solver for a group of strict(non-strict)linear matrix inequalities over a multi-agent network,where each agent only knows one inequality,and all agents co-operate to reach a consensus solution in the intersection of all the feasible regions.The formulation is transformed into a distributed optimization problem by introducing slack variables and consensus constraints.Then,by the primal–dual methods,a distributed algorithm is proposed with the help of projection operators and derivative feedback.Finally,the convergence of the algorithm is analyzed,followed by illustrative simulations.
基金Project supported by the Science and Technology Project from State Grid Zhejiang Electric Power Co.,Ltd.,China(No.5211JY20001Q)。
文摘In this paper,the optimization problem subject to N nonidentical closed convex set constraints is studied.The aim is to design a corresponding distributed optimization algorithm over the fixed unbalanced graph to solve the considered problem.To this end,with the push-sum framework improved,the distributed optimization algorithm is newly designed,and its strict convergence analysis is given under the assumption that the involved graph is strongly connected.Finally,simulation results support the good performance of the proposed algorithm.
基金This work was supported by the NNSF of China[grant number 61174071]by 973 Program[grant number 2014CB845301/2/3].
文摘The state-based potential game is discussed and a game-based approach is proposed for distributed optimization problem in this paper.A continuous-time model is employed to design the state dynamics and learning algorithms of the state-based potential game with Lagrangian multipliers as the states.It is shown that the stationary state Nash equilibrium of the designed game contains the optimal solution of the optimization problem.Moreover,the convergence and stability of the learning algorithms are obtained for both undirected and directed communication graph.Additionally,the application to plug-in electric vehicle management is also discussed.
