This paper proposes a distributed optimization framework for solving nonlinear programming problems with separable objective function and local constraints. Our novel approach is based on first reformulating the origi...
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ISBN:
(纸本)9781538613955
This paper proposes a distributed optimization framework for solving nonlinear programming problems with separable objective function and local constraints. Our novel approach is based on first reformulating the original problem as an unconstrained optimization problem using continuously differentiable exact penalty function methods and then using gradient based optimization algorithms. The reformulation is based on replacing the Lagrange multipliers in the augmented Lagrangian of the original problem with Lagrange multiplier functions. The problem of calculating the gradient of the penalty function is challenging as it is non-distributed in general even if the original problem is distributed. We show that we can reformulate this problem as a distributed, unconstrained convex optimization problem. The proposed framework opens new opportunities for the application of various distributed algorithms designed for unconstrained optimization.
This paper considers distributed online optimization with time-varying coupled inequality constraints. The global objective function is composed of local convex cost and regularization functions and the coupled constr...
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ISBN:
(数字)9781728113982
ISBN:
(纸本)9781728113999
This paper considers distributed online optimization with time-varying coupled inequality constraints. The global objective function is composed of local convex cost and regularization functions and the coupled constraint function is the sum of local convex constraint functions. A distributed online primal-dual mirror descent algorithm is proposed to solve this problem, where the local cost, regularization, and constraint functions are held privately and revealed only after each time slot. We first derive regret and constraint violation bounds for the algorithm and show how they depend on the stepsize sequences, the accumulated variation of the comparator sequence, the number of agents, and the network connectivity. As a result, we prove that the algorithm achieves sublinear dynamic regret and constraint violation if the accumulated variation of the optimal sequence also grows sublinearly. We also prove that the algorithm achieves sublinear static regret and constraint violation under mild conditions. In addition, smaller bounds on the static regret are achieved when the objective functions are strongly convex. Finally, numerical simulations are provided to illustrate the effectiveness of the theoretical results.
Coordinated control of a cluster of buildings can lead to reduced energy usage and demand charge. However, it requires individual buildings to share local data, e.g., their energy demands. The leak of such data could ...
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ISBN:
(纸本)9781538613955
Coordinated control of a cluster of buildings can lead to reduced energy usage and demand charge. However, it requires individual buildings to share local data, e.g., their energy demands. The leak of such data could potentially be used by third parties to infer sensitive information such as occupancy that could be used to the detriment of building occupants. In this paper, using the notion of differential privacy, a distributed algorithm based on the Alternating Direction Method of Multiplier (ADMM) algorithm is proposed for the coordinated control of building clusters that can provide guaranteed levels of privacy for individual buildings by adding noises to the data being exchanged. Theoretical bounds on the strength of noises needed to achieve given privacy levels are derived, and the performance suboptimality caused by the added noise is demonstrated through simulations.
In this paper, we propose a scalable distributed algorithm for double-layered multi-agent network to cooperatively find the least square solutions to an over-determined linear equation. Compared with existing consensu...
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ISBN:
(纸本)9781538679012;9781538679265
In this paper, we propose a scalable distributed algorithm for double-layered multi-agent network to cooperatively find the least square solutions to an over-determined linear equation. Compared with existing consensus-based distributed linear equation solvers, the double-layered network structure allows us to implement two types of coordination, namely consensus and conservation, simultaneously. As a result, the proposed algorithm has achieved better scalability in the sense that each agent does not need to know a full row of the overall equation. The convergence of our algorithm is exponential, which has been validated by both analytical proof and numerical simulations.
We present fast and efficient randomized distributed algorithms to find Hamiltonian cycles in random graphs. In particular, we present a randomized distributed algorithm for the G(n,p) random graph model, with number ...
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ISBN:
(纸本)9781538668719
We present fast and efficient randomized distributed algorithms to find Hamiltonian cycles in random graphs. In particular, we present a randomized distributed algorithm for the G(n,p) random graph model, with number of nodes n and p = cln n/n(delta) (for any constant 0 < delta <= 1 and for a suitably large constant c > 0), that finds a Hamiltonian cycle with high probability in O(n(delta)) rounds.(1) Our algorithm works in the (synchronous) CONGEST model (i.e., only 0(log n) sized messages are communicated per edge per round) and its computational cost per node is sublinear (in n) per round and is fully-distributed (each node uses only o(n) memory and all nodes' computations are essentially balanced). Our algorithm improves over the previous best known result in terms of both the running time as well as the edge sparsity of the graphs where it can succeed;in particular, the denser the random graph, the smaller is the running time.
This paper addresses a class of constrained optimization problems over networks in which local cost functions and constraints can be nonconvex. We propose an asynchronous distributed optimization algorithm, relying on...
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ISBN:
(纸本)9783952426982
This paper addresses a class of constrained optimization problems over networks in which local cost functions and constraints can be nonconvex. We propose an asynchronous distributed optimization algorithm, relying on the centralized Method of Multipliers, in which each node wakes up in an uncoordinated fashion and performs either a descent step on a local Augmented Lagrangian or an ascent step on the local multiplier vector. These two phases are regulated by a distributed logic-AND, which allows nodes to understand when the descent on the (whole) Augmented Lagrangian is sufficiently small. We show that this distributed algorithm is equivalent to a block coordinate descent algorithm for the minimization of the Augmented Lagrangian followed by an update of the whole multiplier vector. Thus, the proposed algorithm inherits the convergence properties of the Method of Multipliers.
distributed linear complementarity problems are important with many applications. A continuous-time nonsmooth algorithm is proposed in a distributed manner to solve the problem with positive definite matrices. Then ex...
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ISBN:
(纸本)9781538660898
distributed linear complementarity problems are important with many applications. A continuous-time nonsmooth algorithm is proposed in a distributed manner to solve the problem with positive definite matrices. Then existence and uniqueness of the solution to the proposed algorithm are analyzed and its exponential convergence is achieved. Moreover, simulations are also given for illustration.
Motivated by broad applications in computer science and engineering, we study distributed algorithms for optimization problems over a network of nodes, where the goal is to optimize a global objective composed of a su...
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ISBN:
(纸本)9781538654286
Motivated by broad applications in computer science and engineering, we study distributed algorithms for optimization problems over a network of nodes, where the goal is to optimize a global objective composed of a sum of local functions. In solving such problems, we propose an algorithm, namely, distributed aggregated stochastic gradient method, which only requires local computation and communication. Our main contribution is to show that the proposed algorithm achieves a linear convergence rate to the neighborhood of the problem solution. In particular, we study the rate of convergence of the algorithm without requiring the Lipschitz continuity of local functions, as often assumed in distributed stochastic gradient methods. In addition, we provide simulations to show that our method outperforms distributed stochastic gradient methods in solving the important linear regression problems over networks.
In this paper, we propose a fully distributed algorithm for second-order continuous-time multi-agent systems to solve the distributed optimization problem. The global objective function is a sum of private cost functi...
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ISBN:
(纸本)9781538613955
In this paper, we propose a fully distributed algorithm for second-order continuous-time multi-agent systems to solve the distributed optimization problem. The global objective function is a sum of private cost functions associated with the individual agents and the interaction between agents is described by a weighted undirected graph. We show the exponential convergence of the proposed algorithm if the underlying graph is connected, each private cost function is locally gradient-Lipschitz- continuous, and the global objective function is restricted strongly convex with respect to the global minimizer. Moreover, to reduce the overall need of communication, we then propose a dynamic event-triggered communication mechanism that is free of Zeno behavior. It is shown that the exponential convergence is achieved if the private cost functions are also globally gradient-Lipschitz- continuous. Numerical simulations are provided to illustrate the effectiveness of the theoretical results.
A distributed algorithm is introduced, which dispatches power for radial electric networks while also accounting for heterogeneous demand functions, demonstrating computational feasibility, and respecting the physical...
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ISBN:
(数字)9781728104072
ISBN:
(纸本)9781728104089
A distributed algorithm is introduced, which dispatches power for radial electric networks while also accounting for heterogeneous demand functions, demonstrating computational feasibility, and respecting the physical limits of the system. The distributed economic dispatch enables small end-users to aggregate themselves such that they can communicate their diverse preferences to the local substation. Unlike other approaches proposed in the literature, the distributed algorithm introduced here converges to an optimal solution with only two sweeps of information exchange once with parent nodes and another time with children nodes. A proof-of-concept example is demonstrated on a 46-bus system under varying levels of DERs, followed by a discussion of the technical and economic benefits of using the distributed algorithm.
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