NEXT：网络内非凸优化
NEXT: In-Network Nonconvex Optimization
AI总结：
本文提出了一种用于多智能体网络中非凸分布式优化的算法框架，通过动态共识机制分配计算，结合递推凸近似技术，实现非凸问题的渐近收敛。
摘要：
我们研究了具有时间变化（非对称）连通性的多智能体网络中的非凸分布式优化问题。我们引入了首个用于分布式最小化光滑（可能非凸且非可分离）函数（智能体的总效用）与凸（可能非光滑且非可分离）正则化项之和的算法框架。后者通常用于强制解具有某些结构，通常为稀疏性。所提出的方法基于递推凸近似技术，并利用动态共识作为机制来在智能体之间分配计算：每个智能体首先解决（可能不精确）非凸原始问题的局部凸近似，然后进行局部平均操作。建立了非凸问题渐近收敛到（ stationary ）解的理论。我们的算法框架随后被定制到多个领域的多种凸和非凸问题中，包括信号处理、通信、网络和机器学习。数值结果表明，新方法在凸和非凸问题上都优于现有分布式算法。
英文摘要：
We study nonconvex distributed optimization in multi-agent networks with time-varying (nonsymmetric) connectivity. We introduce the first algorithmic framework for the distributed minimization of the sum of a smooth (possibly nonconvex and nonseparable) function - the agents' sum-utility - plus a convex (possibly nonsmooth and nonseparable) regularizer. The latter is usually employed to enforce some structure in the solution, typically sparsity. The proposed method hinges on successive convex approximation techniques while leveraging dynamic consensus as a mechanism to distribute the computation among the agents: each agent first solves (possibly inexactly) a local convex approximation of the nonconvex original problem, and then performs local averaging operations. Asymptotic convergence to (stationary) solutions of the nonconvex problem is established. Our algorithmic framework is then customized to a variety of convex and nonconvex problems in several fields, including signal processing, communications, networking, and machine learning. Numerical results show that the new method compares favorably to existing distributed algorithms on both convex and nonconvex problems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
