Distributed non-smooth resource allocation over a network

• Networked systems are common and crucial. Oneof the canonical problems in such systems is distributed resourceallocation. From this rather broad class of problems, weconsider a convex non-smooth resource allocation problem witha global resource constraint. Specifically, the objective functionis separable and consists of a sum of convex functions, eachassociated with a node in a given network. Each component ofthe objective depends on a single variable local to the associatednode and the sum of all local variables must remain constantat all times. For scalability, we constrain the nodes to onlycommunicate and exchange resources with their immediateneighbors. We propose an algorithm that combines subgradientoptimization with distributed averaging. Starting the algorithmfrom a feasible point, the nodes iteratively exchange resourceswith their neighbors to get close to the optimal set whilesatisfying the total resource constraint at all times.We show thatunder mild technical conditions the algorithm converges in anepsilon-sense, as long as the stepsize is chosen sufficiently smalland the distributed averaging process is sufficiently accurate.We derive expressions for how the stepsize and the number ofconsensus iterations affect the accuracy of the final result.

Subject headings

TEKNIK OCH TEKNOLOGIER  -- Elektroteknik och elektronik -- Reglerteknik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Electrical Engineering, Electronic Engineering, Information Engineering -- Control Engineering (hsv//eng)

Publication and Content Type

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