On the Convergence of a Distributed Augmented Lagrangian Method for Nonconvex Optimization

Chatzipanagiotis, Nikolaos; Zavlanos, Michael M.

doi:10.1109/tac.2017.2658438

Cited by 49 publications

(50 citation statements)

References 48 publications

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“…In the relaxed optimization problem, there only exist linear constraints, however, the recursive feasibility of the solution can't be guaranteed. In the second step, the ADAL method [1] is applied to solve the relaxed optimization problem in a decentralized manner. Specifically, each individual zone can determine its local decision variables by solving a smallscale subproblem in parallel at each iteration.…”

Section: Hvac Energy Cost Optimization For a Multi-zonementioning

confidence: 99%

“…However, the recursive feasibility of the solution cannot be guaranteed. In the second step, an ADAL method [1] is applied to solve the nonconvex relaxed optimization problem in a decentralized manner. Last but very important, the third step is focused on recovering the recursive feasibility of the solution for (P1).…”

Section: Decentralized Approachmentioning

confidence: 99%

“…The main contributions of the paper are summarized as follows. Based on decentralized optimization for nonconvex problems with some special structures [1], [21], an efficient decentralized approach for the control of multi-zone HVAC systems is developed in this paper. This decentralized approach mainly contains three steps.…”

Section: Introductionmentioning

confidence: 99%

“…In the relaxed optimization problem, there only exist linear constraints, however, the recursive feasibility of the solution can't be guaranteed. In the second step, an Accelerated Distributed Augmented Lagrangian (ADAL) method proposed in [1] is applied to solve the nonconvex relaxed optimization problem with only linear constraints. Last but very important, the recursive feasibility of the solution is recovered from the optimal solution of the relaxed optimization problem through an heuristic method.…”

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: Hvac Energy Cost Optimization For a Multi-zonementioning

confidence: 99%

Section: Decentralized Approachmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Yong

Spanos

2020

IEEE Trans. Automat. Sci. Eng.

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“…A few early examples of (non-stochastic or deterministic) distributed non-convex optimization algorithms include the Distributed Approximate Dual Subgradient (DADS) Algorithm [8], NonconvEx primal-dual SpliTTing (NESTT) algorithm [9], and the Proximal Primal-Dual Algorithm (Prox-PDA) [10]. More recently, a non-convex version of the accelerated distributed augmented Lagrangians (ADAL) algorithm is presented in [11] and successive convex approximation (SCA)-based algorithms such as iNner cOnVex Approximation (NOVA) and in-Network succEssive conveX approximaTion algorithm (NEXT) are given in [12] and [13], respectively. References [14]- [16] provide several distributed alternating direction method of multipliers (ADMM) based non-convex optimization algorithms.…”

Section: Taoyang@untedumentioning

confidence: 99%

Distributed Stochastic Gradient Method for Non-Convex Problems with Applications in Supervised Learning

George

Yang

Bai

et al. 2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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We develop a distributed stochastic gradient descent algorithm for solving non-convex optimization problems under the assumption that the local objective functions are twice continuously differentiable with Lipschitz continuous gradients and Hessians. We provide sufficient conditions on step-sizes that guarantee the asymptotic mean-square convergence of the proposed algorithm. We apply the developed algorithm to a distributed supervised-learning problem, in which a set of networked agents collaboratively train their individual neural nets to recognize handwritten digits in images. Results indicate that all agents report similar performance that is also comparable to the performance of a centrally trained neural net. Numerical results also show that the proposed distributed algorithm allows the individual agents to recognize the digits even though the training data corresponding to all the digits is not locally available to each agent.

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Analysis of the Alternating Direction Method of Multipliers for Nonconvex Problems

Harwood

2021

SN Oper. Res. Forum

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This work investigates the theoretical performance of the alternating-direction method of multipliers (ADMM) as it applies to nonconvex optimization problems, and in particular, problems with nonconvex constraint sets. The alternating direction method of multipliers is an optimization method that has largely been analyzed for convex problems. The ultimate goal is to assess what kind of theoretical convergence properties the method has in the nonconvex case, and to this end, theoretical contributions are twofold. First, this work analyzes the method with local optimal solution of the ADMM subproblems, which contrasts with much analysis that requires global solutions of the subproblems. Such a consideration is important to practical implementations. Second, it is established that the method still satisfies a local convergence result. The work concludes with some more detailed discussion of how the analysis relates to previous work.

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On the Convergence of a Distributed Augmented Lagrangian Method for Nonconvex Optimization

Cited by 49 publications

References 48 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 Stochastic Gradient Method for Non-Convex Problems with Applications in Supervised Learning

Analysis of the Alternating Direction Method of Multipliers for Nonconvex Problems

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