This paper investigates online distributed optimization within multi-agent systems under inequality constraints. Agents are allowed to exchange local data with their immediate neighbors through a time-varying digraph ...
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This paper investigates online distributed optimization within multi-agent systems under inequality constraints. Agents are allowed to exchange local data with their immediate neighbors through a time-varying digraph and perform computations, aiming to minimize a collective objective function. Considering that the communication capacity of multi-agent systems is often limited in practical applications, a random quantizer is introduced to reduce the transmission bits when agents exchange information over the network. In this study, we specifically consider the scenario where the cost function is stronglypseudoconvex. To handle these problems, a quantized distributed online projection-free optimization algorithm is developed for the stronglypseudoconvex problem with an inequality constraint set. The performance of the algorithm is evaluated using the expectation of dynamic regret. Provided that the graph satisfies certain mild conditions, it has been demonstrated that the bound for each dynamic regret function increases at a sublinear rate. A simulation example is presented to illustrate the validity of our theoretical results.
This paper studies an online distributed optimization problem over multi-agent *** this problem,the goal of agents is to cooperatively minimize the sum of locally dynamic cost *** from most existing works on distribut...
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This paper studies an online distributed optimization problem over multi-agent *** this problem,the goal of agents is to cooperatively minimize the sum of locally dynamic cost *** from most existing works on distributed optimization,here we consider the case where the cost function is stronglypseudoconvex and real gradients of objective functions are not *** handle this problem,an online zeroth-order stochastic optimization algorithm involving the single-point gradient estimator is *** the algorithm,each agent only has access to the information associated with its own cost function and the estimate of the gradient,and exchange local state information with its immediate neighbors via a time-varying *** performance of the algorithm is measured by the expectation of dynamic *** mild assumptions on graphs,we prove that if the cumulative deviation of minimizer sequence grows within a certain rate,then the expectation of dynamic regret grows ***,a simulation example is given to illustrate the validity of our results.
In this paper we obtain first and second-order optimality conditions for an isolated minimum of order two for the problem with inequality constraints and a set constraint. First-order sufficient conditions are derived...
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In this paper we obtain first and second-order optimality conditions for an isolated minimum of order two for the problem with inequality constraints and a set constraint. First-order sufficient conditions are derived in terms of generalized convex functions. In the necessary conditions we suppose that the data are continuously differentiable. A notion of strongly KT invex inequality constrained problem is introduced. It is shown that each Kuhn-Tucker point is an isolated global minimizer of order two if and only if the problem is strongly KT invex. The article could be considered as a continuation of [I. Ginchev, V.I. Ivanov, Second-order optimality, conditions for problems with C-1 data, J. Math. Anal. Appl. 340 (2008) 646-657]. (C) 2009 Elsevier Inc. All rights reserved.
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