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A distributed Network System for Nonsmooth Coupled-Constrained optimization

IEEE TRANSACTIONS ON NETWORK SCIENCE AND ENGINEERING 2022年第5期9卷 3691-3700页

作者： Wang, Xiaoxuan Yang, Shaofu Guo, Zhenyuan Wen, Shiping Huang, Tingwen Hunan Univ Sch Math Hunan Prov Key Lab Intelligent Informat Proc & Ap Changsha 410082 Hunan Peoples R China Southeast Univ Sch Comp Sci & Engn Nanjing 211189 Peoples R China Univ Technol Sydney Ctr Artificial Intelligence Fac Engn Informat Technol Ultimo NSW 2007 Australia Texas A&M Univ Qatar Sci Program Doha 23874 Qatar

This paper addresses a class of distributed nonsmooth optimization problems whose objective function is a sum of convex local objective functions subjected to local set constraints and heterogeneous coupled constraints, including inequality and equality ones. To settle the problem, based on the consensus protocol for the Lagrangian multipliers of coupled constraints, we propose a distributed multi-agent network system with projected output feedback, which is different from the common projected primal-dual subgradient flow. It is proved that the output vector of the system is convergent to the optimal solution of the optimization problem from any initial state over connected communication networks. Finally, the effectiveness of the system is illustrated via two numerical examples.

关键词： optimization Linear programming Output feedback Consensus protocol Network systems Eigenvalues and eigenfunctions convex functions Consensus protocol coupled constraint differential inclusions distributed convex optimization multi-agent network

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distributed Consensus optimization in Multiagent Networks With Time-Varying Directed Topologies and Quantized Communication

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IEEE TRANSACTIONS ON CYBERNETICS 2017年第8期47卷 2044-2057页

作者： Li, Huaqing Huang, Chicheng Chen, Guo Liao, Xiaofeng Huang, Tingwen Southwest Univ Coll Elect & Informat Engn Chongqing 400715 Peoples R China Univ Newcastle Sch Elect Engn & Comp Sci Sydney NSW 2308 Australia Texas A&M Univ Qatar Doha 23874 Qatar

This paper considers solving a class of optimization problems which are modeled as the sum of all agents' convex cost functions and each agent is only accessible to its individual function. Communication between agents in multiagent networks is assumed to be limited: each agent can only interact information with its neighbors by using time-varying communication channels with limited capacities. A technique which overcomes the limitation is to implement a quantization process to the interacted information. The quantized information is first encoded as a binary sequence at the side of each agent before sending. After the binary sequence is received by the neighboring agent, corresponding decoding scheme is utilized to resume the original information with a certain degree of error which is caused by the quantization process. With the availability of each agent's encoding states (associated with its out-channels) and decoding states (associated with its in-channels), we devise a set of distributed optimization algorithms that generate two iterative sequences, one of which converges to the optimal solution and the other of which reaches to the optimal value. We prove that if the parameters satisfy some mild conditions, the quantization errors are bounded and the consensus optimization can be achieved. How to minimize the number of quantization level of each connected communication channel in fixed networks is also explored thoroughly. It is found that, by properly choosing system parameters, one bit information exchange suffices to ensure consensus optimization. Finally, we present two numerical simulation experiments to illustrate the efficacy of the algorithms as well as to validate the theoretical findings.

关键词： Directed time-varying topology distributed convex optimization multiagent systems quantization communication subgradient algorithm

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distributed Bisection Method for Economic Power Dispatch in Smart Grid

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IEEE TRANSACTIONS ON POWER SYSTEMS 2015年第6期30卷 3024-3035页

作者： Xing, Hao Mou, Yuting Fu, Minyue Lin, Zhiyun Zhejiang Univ State Key Lab Ind Control Technol Hangzhou 310027 Zhejiang Peoples R China Zhejiang Univ Dept Control Sci & Engn Hangzhou 310027 Zhejiang Peoples R China Univ Newcastle Sch Elect Engn & Comp Sci Callaghan NSW 2308 Australia Zhejiang Univ Coll Elect Engn Hangzhou 310027 Zhejiang Peoples R China

In this paper, we present a fully distributed bisection algorithm for the economic dispatch problem (EDP) in a smart grid scenario, with the goal to minimize the aggregated cost of a network of generators, which cooperatively furnish a given amount of power within their individual capacity constraints. Our distributed algorithm adopts the method of bisection, and is based on a consensus-like iterative method, with no need for a central decision maker or a leader node. Under strong connectivity conditions and allowance for local communications, we show that the iterative solution converges to the globally optimal solution. Furthermore, two stopping criteria are presented for the practical implementation of the proposed algorithm, for which sign consensus is defined. Finally, numerical simulations based on the IEEE 14-bus and 118-bus systems are given to illustrate the performance of the algorithm.

关键词： Consensus distributed algorithm distributed convex optimization economic power dispatch smart grid

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Stabilized distributed online mirror descent for multi-agent optimization

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KNOWLEDGE-BASED SYSTEMS 2024年 304卷

作者： Wu, Ping Huang, Heyan Lu, Haolin Liu, Zhengyang Beijing Inst Technol Sch Comp Sci & Technol Beijing 100081 Peoples R China

In the domain of multi-agent networks, distributed online mirror descent (DOMD) and distributed online dual averaging (DODA) play pivotal roles as fundamental algorithms for distributed online convex optimization. However, in contrast to DODA, DOMD fails when employed with a dynamic learning rate sequence. To bridge this gap, we introduce two novel variants of DOMD by incorporating a distributed stabilization step in primal space and dual space, respectively. We demonstrate that our stabilized DOMD algorithms achieve a sublinear bound with a sequence of dynamic learning rates. We further evolve our dual-stabilized DOMD by integrating a lazy communicated subgradient descent step, resulting in a re-indexed DODA. This establishes a connection between the two types of distributed algorithms, which enhances our understandings of distributed optimization. Moreover, we extend our proposed algorithms to handle the case of exponentiated gradient, where the iterate is constrained within a simplex probability. Finally, we conduct extensive numerical simulations to validate our theoretical analysis.

关键词： distributed convex optimization Online mirror descent Online dual averaging Dynamic learning rate Stabilization step Multi-agent network

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Gossip-based distributed stochastic mirror descent for constrained optimization

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NEURAL NETWORKS 2024年 175卷 106291页

作者： Fang, Xianju Zhang, Baoyong Yuan, Deming Nanjing Univ Sci & Technol Sch Automat Nanjing 210094 Jiangsu Peoples R China

This paper considers a distributed constrained optimization problem over a multi -agent network in the nonEuclidean sense. The gossip protocol is adopted to relieve the communication burden, which also adapts to the constantly changing topology of the network. Based on this idea, a gossip -based distributed stochastic mirror descent (GB-DSMD) algorithm is proposed to handle the problem under consideration. The performances of GB-DSMD algorithms with constant and diminishing step sizes are analyzed, respectively. When the step size is constant, the error bound between the optimal function value and the expected function value corresponding to the average iteration output of the algorithm is derived. While for the case of the diminishing step size, it is proved that the output of the algorithm uniformly approaches to the optimal value with probability 1. Finally, as a numerical example, the distributed logistic regression is reported to demonstrate the effectiveness of the GB-DSMD algorithm.

关键词： Stochastic mirror descent distributed constrained optimization distributed convex optimization Gossip algorithm

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distributed neurodynamic approaches to nonsmooth optimization problems with inequality and set constraints

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COMPLEX & INTELLIGENT SYSTEMS 2022年第6期8卷 5511-5530页

作者： Luan, Linhua Wen, Xingnan Qin, Sitian Harbin Inst Technol Dept Math Weihai Peoples R China

In this paper, neurodynamic approaches are proposed for solving nonsmooth distributed optimization problems under inequality and set constraints, that is to find the solution that minimizes the sum of local cost functions. A continuous-time neurodynamic approach is designed and its state solution exists globally and converges to an optimal solution of the corresponding distributed optimization problem. Then, a neurodynamic approach with event-triggered mechanism is considered for the purpose of saving communication costs, and then, the convergence and its Zeno-free property are proved. Moreover, to realize the practical application of the neurodynamic approach, a discrete-time neurodynamic approach is proposed to solve nonsmooth distributed optimization problems under inequality and set constraints. It is rigorously proved that the iterative sequence generated by the discrete-time neurodynamic approach converges to the optimal solution set of the distributed optimization problem. Finally, numerical examples are solved to demonstrate the effectiveness of the proposed neurodynamic approaches, and the neurodynamic approach is further applied to solve the ill-conditioned Least Absolute Deviation problem and the load sharing optimization problem.

关键词： distributed convex optimization Penalty method Multi-agent system Projection operator Event-triggered mechanism

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distributed optimal resource allocation over networked systems and use of an ε-exact penalty function

Distributed optimal resource allocation over networked syste...

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14th IFAC Symposium on Large Scale Complex Systems - Theory and Applications (IFAC LSS)

作者： Kia, Solmaz S. Univ Calif Irvine Dept Mech & Aerosp Engn Irvine CA 92717 USA

We consider an optimal resource allocation problem over networked systems with connected graph communication topologies. The global cost function in this problem is the sum of local convex cost functions of the agents and the constraints are the affine demand equation and local box constraints on the decision variable of each agent. To solve this problem, we propose a novel distributed continuous-time algorithm. Our solution takes advantage of a smooth epsilon-exact penalty function method to handle the local box inequality constrains. In this paper, we also obtain a lower bound on the admissible values of the weight of our penalty function in terms of the size of the gradient of local cost functions. Then, we discuss how agents can use this lower bound to determine the penalty function weight in a distributed manner. Simulations illustrate our results. (C) 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

关键词： cooperative control distributed convex optimization distributed optimal resource allocation smooth penalty functions

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Coordinate Dual Averaging for Decentralized Online optimization With Nonseparable Global Objectives

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IEEE TRANSACTIONS ON CONTROL OF NETWORK SYSTEMS 2018年第1期5卷 34-44页

作者： Lee, Soomin Nedic, Angelia Raginsky, Maxim Duke Univ Dept Mech Engn & Mat Sci Durham NC 27708 USA Univ Illinois Champaign IL 61820 USA Univ Illinois Dept Ind & Enterprise Syst Engn Urbana IL 61801 USA Univ Illinois Dept Elect & Comp Engn Urbana IL 61801 USA

We consider a decentralized online convex optimization problem in a network of agents, where each agent controls only a coordinate (or a part) of the global decision vector. For such a problem, we propose two decentralized variants (ODA-C and ODA-PS) of Nesterov's primal-dual algorithm with dual averaging. In ODA-C, to mitigate the disagreements on the primal-vector updates, the agents implement a generalization of the local information-exchange dynamics recently proposed by Li and Marden [1] over a static undirected graph. In ODA-PS, the agents implement the broadcast-based push-sum dynamics [2] over a time-varying sequence of uniformly connected digraphs. We show that the regret bounds in both cases have sublinear growth of O(root T), with the time horizon T, when the stepsize is of the form 1/root t and the objective functions are Lipschitz-continuous convex functions with Lipschitz gradients. We also implement the proposed algorithms on a sensor network to complement our theoretical analysis.

关键词： distributed convex optimization dual averaging multiagent systems online optimization

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distributed Frank-Wolfe under Pipelined Stale Synchronous Parallelism 3

Distributed Frank-Wolfe under Pipelined Stale Synchronous Pa...

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IEEE International Conference on Big Data

作者： Tran, Nam-Luc Peel, Thomas Skhiri, Sabri EURA NOVA Mt St Guibert France

ISBN: (纸本)9781479999255

Iterative-convergent algorithms represent an important family of applications in big data analytics. These are typically run on distributed processing frameworks deployed on a cluster of machines. On the other hand, we are witnessing the move towards data center operating systems (OS), where resources are unified by a resource manager and processing frameworks coexist with each other. In this context, different processing framework job tasks can be scheduled on the same machine and slow down a worker (straggler problem). Existing work has shown that an iteration model with relaxed consistency such as the Stale Synchronous Parallel (SSP) model, while still guaranteeing convergence, is able to cope with stragglers. In this paper we propose a model for the integration of the SSP model on a pipelined distributed processing framework. We then apply SSP on a distributed version of the Frank-Wolfe algorithm. We theoretically show its sparsity bounds and convergence under SSP. Finally, we experimentally show that the Frank-Wolfe algorithm applied on LASSO regression under SSP is able to converge faster than its BSP counterpart, especially under load conditions similar to those encountered in a data center OS.

关键词： stale synchronous parallel distributed convex optimization Frank-Wolfe LASSO regression parameter server big data

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distributed Sub-gradient Algorithms with Limited Communications 53

Distributed Sub-gradient Algorithms with Limited Communicati...

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53rd Asilomar Conference on Signals, Systems, and Computers (ACSSC)

作者： Rini, Stefano Rao, Milind Goldsmith, Andrea Stanford Univ Elect Engn Stanford CA 94305 USA Natl Chiao Tung Univ Hsinchu Taiwan

ISBN: (纸本)9781728143002

We consider the distributed convex optimization scenario in which nodes in a network collectively find the minimum of a function utilizing only local communications and computations. Various sub-gradient algorithms have been developed for this optimization setting for the case in which the global function factorizes as the sum of local functions to be distributed to the nodes in network, including the distributed (i) online gradient descent, (ii) Nesterov gradient descent, and (iii) dual averaging algorithms. Generally speaking, these subgradient algorithms assume that, in each communication round, nodes can exchange messages of size comparable to that of the optimization variable. For many high-dimensional optimization problems, this communication requirement is beyond the capabilities of the communication network supporting the distributed optimization. For this reason, we propose a dimensionality reduction technique based on random projections to adapt these distributed optimization algorithms to networks with communication links of limited capacity. In particular, we analyze the performance of the proposed dimensionality reduction technique for the three algorithms above, i.e. (i)-(iii). Numerical simulations are presented that illustrate the performance of the proposed approach for these three algorithms.

关键词： distributed convex optimization Decentralized methods Gradient descent methods Dual averaging Nesterov gradient acceleration Random projections

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