Distributed Difference of Convex Optimization
<|reference_start|>Distributed Difference of Convex Optimization: In this article, we focus on solving a class of distributed optimization problems involving $n$ agents with the local objective function at every agent $i$ given by the difference of two convex functions $f_i$ and $g_i$ (difference-of-convex (DC) form), where $f_i$ and $g_i$ are potentially nonsmooth. The agents communicate via a directed graph containing $n$ nodes. We create smooth approximations of the functions $f_i$ and $g_i$ and develop a distributed algorithm utilizing the gradients of the smooth surrogates and a finite-time approximate consensus protocol. We term this algorithm as DDC-Consensus. The developed DDC-Consensus algorithm allows for non-symmetric directed graph topologies and can be synthesized distributively. We establish that the DDC-Consensus algorithm converges to a stationary point of the nonconvex distributed optimization problem. The performance of the DDC-Consensus algorithm is evaluated via a simulation study to solve a nonconvex DC-regularized distributed least squares problem. The numerical results corroborate the efficacy of the proposed algorithm.<|reference_end|>
@article{khatana2024distributed,
    title={Distributed Difference of Convex Optimization},
    author={Vivek Khatana, Murti V. Salapaka},
    journal={arXiv preprint arXiv:2407.16728},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.16728},
    primaryClass={math.OC cs.AI cs.DC cs.SY eess.SY}
}