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Distributed coordination for nonsmooth convex optimization via saddle-point dynamics. (arXiv:1606.09298v2 [math.OC] UPDATED)
来源于:arXiv
This paper considers continuous-time coordination algorithms for networks of
agents that seek to collectively solve a general class of nonsmooth convex
optimization problems with an inherent distributed structure. Our algorithm
design builds on the characterization of the solutions of the nonsmooth convex
program as saddle points of an augmented Lagrangian. We show that the
associated saddle-point dynamics are asymptotically correct but, in general,
not distributed because of the presence of a global penalty parameter. This
motivates the design of a discontinuous saddle-point-like algorithm that enjoys
the same convergence properties and is fully amenable to distributed
implementation. Our convergence proofs rely on the identification of a novel
global Lyapunov function for saddle-point dynamics. This novelty also allows us
to identify mild convexity and regularity conditions on the objective function
that guarantee the exponential convergence rate of the proposed algorithms for
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