Gradient-free method for nonsmooth distributed optimization
MetadataShow full item record
In this paper, we consider a distributed nonsmooth optimization problem over a computational multi-agent network. We first extend the (centralized) Nesterov’s random gradient-free algorithm and Gaussian smoothing technique to the distributed case. Then, the convergence of the algorithm is proved. Furthermore, an explicit convergence rate is given in terms of the network size and topology. Our proposed method is free of gradient, which may be preferred by practical engineers. Since only the cost function value is required, our method may suffer a factor up to d (the dimension of the agent) in convergence rate over that of the distributed subgradient-based methods in theory. However, our numerical simulations show that for some nonsmooth problems, our method can even achieve better performance than that of subgradient-based methods, which may be caused by the slow convergence in the presence of subgradient.
Showing items related by title, author, creator and subject.
Li, J.; Wu, Changzhi; Wu, Z.; Long, Q.; Wang, Xiangyu (2014)We consider a distributed optimization problem over a multi-agent network, in which the sum of several local convex objective functions is minimized subject to global convex inequality constraints. We first transform the ...
Chai, Qinqin (2013)In this thesis, we develop new computational methods for three classes of dynamic optimization problems: (i) A parameter identification problem for a general nonlinear time-delay system; (ii) an optimal control problem ...
Performance evaluation of block-diagonal preconditioners for the divergence-conforming B-spline discretization of the Stokes systemCôrtes, A.; Coutinho, A.; Dalcin, L.; Calo, Victor (2014)The recently introduced divergence-conforming B-spline discretizations allow the construction of smooth discrete velocity-pressure pairs for viscous incompressible flows that are at the same time inf-sup stable and pointwise ...