English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper, two distributed multi-proximal primal-dual algorithms areproposed to deal with a class of distributed nonsmooth resource allocationproblems. In these problems, the global cost function is the summation of localconvex and nonsmooth cost functions, each of which consists of one twicedifferentiable function and multiple nonsmooth functions. Communication graphsof underling multi-agent systems are directed and strongly connected but notnecessarily weighted-balanced. The multi-proximal splitting is designed to dealwith the difficulty caused by the unproximable property of the summation ofthose nonsmooth functions. Moreover, it can also guarantee the smoothness ofproposed algorithms. Auxiliary variables in the multi-proximal splitting areintroduced to estimate subgradients of nonsmooth functions. Theoretically, theconvergence analysis is conducted by employing Lyapunov stability theory andintegral input-to-state stability (iISS) theory with respect to set. It showsthat proposed algorithms can make states converge to the optimal point thatsatisfies resource allocation conditions.

Solving A Class of Nonsmooth Resource Allocation Problems with Directed Graphs though Distributed Smooth Multi-Proximal Algorithms