Regularized Primal–Dual Subgradient Method for Distributed Constrained Optimization

Yuan, Deming; Ho, Daniel W. C.; Xu, Shengyuan

doi:10.1109/tcyb.2015.2464255

Cited by 137 publications

(68 citation statements)

References 30 publications

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“…The problem (P1) is a nonlinear and nonconvex optimization problem, which is difficult to find an existing decentralized or distributed method to solve it. Because most of the existing decentralized or distributed methods [18]- [20], [33]- [35], such as distributed primal-dual subgradient methods [18], dual decomposition [19], distributed ADMM [20] are developed for convex optimization problems and some of them can only tackle linear constraints.…”

Section: E the Optimization Problemmentioning

confidence: 99%

“…More specifically, both the system dynamics and the global objective function of the problem are nonlinear and nonconvex. Most of the existing decentralized or distributed methods, such as distributed primal-dual subgradient methods [18], dual decomposition [19], distributed Alternating Direction Method of Multipliers (ADMM) [20] can't be directly applied to solve the problem. Because these decentralized or distributed methods are generally established for convex problems and some of them even can only accommodate linear constraints.…”

Section: Introductionmentioning

confidence: 99%

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HVAC Energy Cost Optimization for a Multizone Building via a Decentralized Approach

Yong

Spanos

2020

IEEE Trans. Automat. Sci. Eng.

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It has been well acknowledged that buildings account for a large proportion of the worlds energy consumption. However, the energy use of buildings, especially the heating, ventilation and air-conditioning (HVAC), is far from being efficient. There still exists a dramatic potential to save energy through improving building energy efficiency. Therefore, this paper studies the control of HVAC system for multi-zone buildings with the objective to reduce energy consumption cost while satisfying thermal comfort. In particular, the thermal couplings due to the heat transfer between the adjacent zones are incorporated in the optimization. Considering that a centralized method is generally computationally prohibitive for large buildings, an efficient decentralized approach is developed, based on the Accelerated Distributed Augmented Lagrangian (ADAL) method [1]. To evaluate the performance of the proposed method, we first compare it with a centralized method, in which the optimal solution of a small-scale problem can be obtained. We find that this decentralized approach can almost approach the optimal solution of the problem. Further, this decentralized approach is compared with the Distributed Token-Based Scheduling Strategy (DTBSS) [2]. The numeric results reveal that when the number of zones is relatively small (less than 20), the two decentralized methods can achieve a comparable performance regarding the cost of the HVAC system. However, with an increase of the number of zones in the building, the proposed decentralized approach demonstrates better performance with a considerable reduction of the total cost. Moreover, the decentralized approach proposed in this paper demonstrate better scalability with less average computation required.Note to Practitioners-Buildings accounts for a large proportion of the worlds energy consumption, especially the HVAC system. How to improve the energy efficiency of HVAC system has been recognized as an important and urgent problem for a sustainable future. Motivated by this important problem, this paper is focused on the intelligent control of HVAC system for multi-zone buildings with the objective to reduce energy consumption cost for the HVAC system while maintaining zone thermal comfort. Considering that a centralized method usually encounters computation difficulties with a large number of zones, this paper aims to develop an efficient decentralized solution. In terms of the problem, there usually exist various couplings between different zones, which both arise from the heat transfer between the neighbouring zones and the operation limits of ).the HVAC system. Moreover, this problem is nonconvex and nonlinear. Therefore, it is generally difficult to find an existing decentralized or distributed method, which are mostly established for convex optimization problems. Motivated by the recent progress on decentralized or distributed optimization for nonconvex problems, this paper proposes an efficient decentralized approach, which mainly contains three steps. In the first step, the o...

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Section: E the Optimization Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

HVAC Energy Cost Optimization for a Multizone Building via a Decentralized Approach

Yong

Spanos

2020

IEEE Trans. Automat. Sci. Eng.

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“…Lemma 2: Let x(t) be a solution of different inclusion (3), and let f : R n → R be a locally Lipschitz continuous and regular function [26]. Then d dt f (x(t)) exists and d dt f (x(t)) ∈L F f (x) almost everywhere.…”

Section: Definitionmentioning

confidence: 99%

“…Under the influence of big data and large-scale systems, distributed optimization and computation have attracted more and more research attention. Both discrete-time algorithms [1]- [3] and continuous-time algorithms [4]- [6] have been given for various distributed optimization problems. The basic idea is that many interconnected agents in a network, having local information W. Deng and Y. Hong are with the School of Mathematical Sciences, University of Chinese Academy of Sciences; Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, information.…”

Section: Introductionmentioning

confidence: 99%

Distributed Computation for Solving the Sylvester Equation Based on Optimization

Deng

Zeng

2020

IEEE Control Syst. Lett.

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This paper solves the Sylvester equation in the form of AX + XB = C in a distributed way, and proposes three distributed continuous-time algorithms for three cases. We start with the basic algorithm for solving a least squares solution of the equation, and then give a simplified algorithm for the case when there is an exact solution to the equation, followed by an algorithm with regularization case. Based on local information and appropriate communication among neighbor agents, we solve the distributed computation problem of the Sylvester equation from the optimization viewpoint, and we prove the convergence of proposed algorithms to an optimal solution in three different cases, with help of the convex optimization and semi-stability. separately, cooperate with their neighbors to exchange information and achieve global goals eventually.With the rapid development of distributed optimization algorithms, the idea of using distributed methods to solve matrix equations has attracted much interest. The Sylvester equation is an important class of matrix equations, which has wide application in control theory, systems theory and many other fields [7]-[10]. For instance, the Sylvester equation plays a significant role in computing invariant subspaces [11], achieving pole assignment [12] and model reduction [13]. There have been many centralized algorithms for solving matrix equations, such as Schur decomposition methods, Krylov-subspace methods, and iterative methods [9], [14]-[16]. However, those centralized algorithms for solving the Sylvester equation AX + XB = C mainly need to deal with the whole two coefficient matrices A and B, which could not be applied directly to many distributed scenarios, including the one we consider in this paper. Besides, the parallel distributed computation for the Sylvester equation [17] could not work only for such local information either, because it needs to transform A and B to real Schur form at first. Recently, there have been several works about solving the linear algebraic equation in the form of Ax = b by various distributed methods [18]-[22]. With the help of a network structure, every node only gets access to the local information, for example, a row [18]-[20] or a column [22]of the matrix A. In [21], there is a double-layered framework for all nodes and it enhances the flexibility of the access to information. There is not much work about solving matrix equations in a distributed way yet. Though we could transform a matrix equation into the form of a linear algebraic equation sometimes, its partition structure has less flexibility to a certain extent. Due to matrix multiplication rules, there are some differences between matrix equations and linear algebraic equations. A class of matrix equations formed as AXB = F was first discussed in [23], with different distributed algorithms according to different partition structures. However, there are no results on the distributed computation of the Sylvester equation, which is more complicated than AXB = F , to our knowledge.The object...

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“…Two application examples are presented to validate the proposed approach: a distributed source localization problem and the parameter estimation of a neural network.Another relevant class of algorithms is that of distributed primal-dual methods (see, e.g. [6,7,8]). Within this framework, an iterative scheme combining dual decomposition and proximal minimization is introduced in [9].…”

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confidence: 99%

A distributed asynchronous method of multipliers for constrained nonconvex optimization

et al. 2019

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This paper presents a fully asynchronous and distributed approach for tackling optimization problems in which both the objective function and the constraints may be nonconvex. In the considered network setting each node is active upon triggering of a local timer and has access only to a portion of the objective function and to a subset of the constraints. In the proposed technique, based on the method of multipliers, each node performs, when it wakes up, either a descent step on a local augmented Lagrangian or an ascent step on the local multiplier vector. Nodes realize when to switch from the descent step to the ascent one through an asynchronous distributed logic-AND, which detects when all the nodes have reached a predefined tolerance in the minimization of the augmented Lagrangian. It is shown that the resulting distributed algorithm is equivalent to a block coordinate descent for the minimization of the global augmented Lagrangian. This allows one to extend the properties of the centralized method of multipliers to the considered distributed framework. Two application examples are presented to validate the proposed approach: a distributed source localization problem and the parameter estimation of a neural network.Another relevant class of algorithms is that of distributed primal-dual methods (see, e.g. [6,7,8]). Within this framework, an iterative scheme combining dual decomposition and proximal minimization is introduced in [9]. Distributed approaches based on the Alternating Directions Method of Multipliers (ADMM) are presented in [10,11,12].Asynchronous communication protocols are a typical requirement in real world networks (see, e.g., [13] and references therein). Several asynchronous version of distributed optimization algorithms have been proposed in literature, a typical example being the class of gossip-based algorithms [14,15]. By building on these works, an asynchronous algorithm based on the Method of Multipliers and accounting for communication failures is introduced in [16]. In [17] an asynchronous ADMM is proposed for a separable, constrained optimization problem. An asynchronous proximal dual algorithm has been presented in [18].Distributed algorithms for nonconvex optimization have started to appear in the literature only recently. In [19] a stochastic gradient method is proposed to minimize the sum of smooth nonconvex functions subject to a constraint known to all agents. In [20] a decentralized Frank-Wolfe method for finding a stationary point of the sum of differentiable and nonconvex functions is given. In [21,22] the authors propose distributed algorithms, respectively for balanced and general directed graphs, based on the idea of tracking the whole function gradient and performing successive convex approximation of the nonconvex cost function. Notice that the approaches in [19,20,21,22] do not deal with local constraints, but only with global ones known to all the agents. A perturbed push-sum algorithm for the unconstrained minimization of the sum of nonconvex smooth functions is give...

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Regularized Primal–Dual Subgradient Method for Distributed Constrained Optimization

Cited by 137 publications

References 30 publications

HVAC Energy Cost Optimization for a Multizone Building via a Decentralized Approach

HVAC Energy Cost Optimization for a Multizone Building via a Decentralized Approach

Distributed Computation for Solving the Sylvester Equation Based on Optimization

A distributed asynchronous method of multipliers for constrained nonconvex optimization

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