Incremental Stochastic Subgradient Algorithms for Convex Optimization

Ram, S. Sundhar; Nedić, Angelia; Veeravalli, Venugopal V.

doi:10.1137/080726380

Cited by 212 publications

(168 citation statements)

References 21 publications

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“…[44], and Ram et al [46,47]. Incremental subgradient methods have convergence properties that are similar in many ways to their gradient counterparts, the most important similarity being the necessity of a diminishing stepsize α k for convergence.…”

Section: Introductionmentioning

confidence: 99%

Incremental proximal methods for large scale convex optimization

2011

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We consider the minimization of a sum m i=1 f i (x) consisting of a large number of convex component functions f i . For this problem, incremental methods consisting of gradient or subgradient iterations applied to single components have proved very effective. We propose new incremental methods, consisting of proximal iterations applied to single components, as well as combinations of gradient, subgradient, and proximal iterations. We provide a convergence and rate of convergence analysis of a variety of such methods, including some that involve randomization in the selection of components. We also discuss applications in a few contexts, including signal processing and inference/machine learning.

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Section: Introductionmentioning

confidence: 99%

Incremental proximal methods for large scale convex optimization

2011

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“…Different from [1]- [5], a dual averaging subgradient algorithm was developed and analyzed for randomized graphs under the assumption that all agents remain in the same closed convex set in [6] and it was shown that the number of iterations were required by their algorithm scales inversely in the spectral gap of the network. Moreover, distributed optimization problems with asynchronous step-sizes or inequality-equality constraints or using other algorithms were studied in [7]- [12] and corresponding conditions were given to ensure the system converge to the optimal point or its neighborhood. However, as in [1]- [5], it was assumed in [6]- [12] that the state sets of agents to be identical or the objective function finally converge to only a neighborhood of the optimal set.…”

Section: Introductionmentioning

confidence: 99%

“…Distributed optimization problems of multi-agent systems appear different kinds of distributed processing issues such as distributed estimation, distributed motion planning, distributed resource allocation and distributed congestion control [1][2][3][4][5][6][7][8][9][10][11][12]. The main focus is to solve a distributed optimization problem where the global objective function is composed of a sum of local objective functions, each of which is only known by one agent.…”

Section: Introductionmentioning

confidence: 99%

Distributed Subgradient Algorithm for Multi-Agent Convex Optimization with Global Inequality and Equality Constraints

Xiao¹

2016

ACM

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Abstract:In this paper, we present an improved subgradient algorithm for solving a general multi-agent convex optimization problem in a distributed way, where the agents are to jointly minimize a global objective function subject to a global inequality constraint, a global equality constraint and a global constraint set. The global objective function is a combination of local agent objective functions and the global constraint set is the intersection of each agent local constraint set. Our motivation comes from networking applications where dual and primal-dual subgradient methods have attracted much attention in the design of decentralized network protocols. Our main focus is on constrained problems where the local constraint sets are identical. Thus, we propose a distributed primal-dual subgradient algorithm, which is based on the description of the primal-dual optimal solutions as the saddle points of the penalty functions. We show that, the algorithm can be implemented over networks with changing topologies but satisfying a standard connectivity property, and allow the agents to asymptotically converge to optimal solution with optimal value of the optimization problem under the Slater's condition.

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“…6] in the context of real wireless sensor networks. There are several possible implementations mostly based on incremental gradients methods [12] which can be deterministic [13] or randomized [14], [15]. Important extensions include the use of projections in order to take into account possible different local constraints [16], and the analysis of the convergence rate and error bounds [17], [18].…”

Section: A Previous Workmentioning

confidence: 99%

Newton-Raphson consensus for distributed convex optimization

Zanella

Varagnolo

Cenedese

et al. 2011

IEEE Conference on Decision and Control and European Control Conference

101

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Abstract-We study the problem of unconstrained distributed optimization in the context of multi-agents systems subject to limited communication connectivity. In particular we focus on the minimization of a sum of convex cost functions, where each component of the global function is available only to a specific agent and can thus be seen as a private local cost. The agents need to cooperate to compute the minimizer of the sum of all costs. We propose a consensus-like strategy to estimate a Newton-Raphson descending update for the local estimates of the global minimizer at each agent. In particular, the algorithm is based on the separation of time-scales principle and it is proved to converge to the global minimizer if a specific parameter that tunes the rate of convergence is chosen sufficiently small. We also provide numerical simulations and compare them with alternative distributed optimization strategies like the Alternating Direction Method of Multipliers and the Distributed Subgradient Method.

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Incremental Stochastic Subgradient Algorithms for Convex Optimization

Cited by 212 publications

References 21 publications

Incremental proximal methods for large scale convex optimization

Incremental proximal methods for large scale convex optimization

Distributed Subgradient Algorithm for Multi-Agent Convex Optimization with Global Inequality and Equality Constraints

Newton-Raphson consensus for distributed convex optimization

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