# Distributed Nonsmooth Robust Resource Allocation with Cardinality Constrained Uncertainty

## TL;DR

This paper introduces a distributed primal-dual algorithm for solving a nonsmooth, robust resource allocation problem with cardinality constrained uncertainty, ensuring convergence to optimal solutions in multi-agent systems.

## Contribution

It develops a novel distributed primal-dual projected algorithm and provides a convergence analysis for solving nonsmooth robust resource allocation with uncertainty.

## Key findings

- Algorithm converges to optimal resource allocation
- Simulation demonstrates efficiency of the proposed method
- Addresses nonsmooth and uncertain resource allocation challenges

## Abstract

A distributed nonsmooth robust resource allocation problem with cardinality constrained uncertainty is investigated in this paper. The global objective is consisted of local objectives, which are convex but nonsmooth. Each agent is constrained in its private convex set and has only the information of its corresponding local objective. The resource allocation condition is subject to the cardinality constrained uncertainty sets. By employing the duality theory of convex optimization, a dual problem of the robust resource allocation problem is presented. For solving this dual problem, a distributed primal-dual projected algorithm is proposed. Theoretically, the convergence analysis by using stability theory of differential inclusions is conducted. It shows that the algorithm can steer the multi-agent system to satisfy resource allocation condition at the optimal solution. In the end, a nontrivial simulation is shown and the results demonstrate the efficiency of the proposed algorithm.