Prescribed-time convergence mechanism has become a prominent research focus in the current field of optimization and control due to its ability to precisely control the target completion time. The recently arisen prescribed-time algorithms for distributed optimization, currently necessitate multi-stage structures to achieve global convergence. This paper introduces two modified zero-gradient-sum algorithms, each based on a multi-stage and a single-stage structural frameworks established in this work. These algorithms are designed to achieve prescribed-time convergence and relax two common yet stringent conditions. This work also bridges the gap in current research on single-stage structured PTDO algorithm. The excellent convergence performance of the proposed algorithms is validated through a case study.
@article{arxiv.2310.18915,
title = {Multi/Single-stage structured zero-gradient-sum approach for prescribed-time optimization},
author = {Shuaiyu Zhou and Yiheng Wei and Jinde Cao and Yang Liu},
journal= {arXiv preprint arXiv:2310.18915},
year = {2023}
}