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arXiv · 2304.02830

A Mixing-Accelerated Primal-Dual Proximal Algorithm for Distributed Nonconvex Optimization

Zichong Ou·Chenyang Qiu·Dandan Wang·Jie Lu
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Abstract

In this paper, we develop a distributed mixing-accelerated primal-dual proximal algorithm, referred to as MAP-Pro, which enables nodes in multi-agent networks to cooperatively minimize the sum of their nonconvex, smooth local cost functions in a decentralized fashion. The proposed algorithm is constructed upon minimizing a computationally inexpensive augmented-Lagrangian-like function and incorporating a time-varying mixing polynomial to expedite information fusion across the network. The convergence results derived for MAP-Pro include a sublinear rate of convergence to a stationary solution and, under the Polyak-Łojasiewics (P-Ł) condition, a linear rate of convergence to the global optimal solution. Additionally, we may embed the well-noted Chebyshev acceleration scheme in MAP-Pro, which generates a specific sequence of mixing polynomials with given degrees and enhances the convergence performance based on MAP-Pro. Finally, we illustrate the competitive convergence speed and communication efficiency of MAP-Pro via a numerical example.

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Zichong Ou, Chenyang Qiu, Dandan Wang, Jie Lu. 2024-03-10. A Mixing-Accelerated Primal-Dual Proximal Algorithm for Distributed Nonconvex Optimization. https://arxiv.org/abs/2304.02830

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