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 Tools annual

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 Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

This article reports an algorithm for multiagent distributed optimization problems with a common decision variable, local linear equality, and inequality, constraints and set constraints with convergence rate guarantees. The algorithm accrues all the benefits of the alternating direction method of multipliers (ADMM) approach. It also overcomes the limitations of existing methods on convex optimization problems with linear inequality, equality, and set constraints by allowing directed communication topologies. Moreover, the algorithm can be synthesized distributively. The developed algorithm has: first, a   $O(1/k) $   rate of convergence, where   $k$   is the iteration counter, when individual functions are convex but not-necessarily differentiable, and second, a geometric rate of convergence to any arbitrary small neighborhood of the optimal solution, when the objective functions are smooth and restricted strongly convex at the optimal solution. The efficacy of the algorithm is evaluated by a comparison with state-of-the-art constrained optimization algorithms in solving a constrained distributed   $\ell _{1}$  -regularized logistic regression problem, and unconstrained optimization algorithms in solving a   $\ell _{1}$  -regularized Huber loss minimization problem. Additionally, a comparison of the algorithm&#x0027;s performance with other algorithms in the literature that utilize multiple communication steps is provided.

DC-DistADMM : ADMM Algorithm for Constrained Optimization Over Directed Graphs