Robust hybrid zero-order optimization algorithms with acceleration via averaging in time
Robust hybrid zero-order optimization algorithms with acceleration via averaging in time
复制标题
鲁棒混合零阶优化算法，通过时间平均加速
DOI：
10.1016/j.automatica.2020.109361
复制
发表时间：
2021
期刊：
影响因子：
6.4
通讯作者：
Li, Na
中科院分区：
文献类型：
--
作者：
Poveda, Jorge I.;Li, Na
本文提出了一类新的鲁棒零阶算法，用于求解具有加速度的实时优化问题。特别地，我们提出了一类极值寻求（ES）动力学，可以普遍地建模为具有重启机构的奇摄动混合动力系统。从这个动力学家族中，我们综合了四种快速求解凸、强凸、约束和无约束优化问题的算法。在每种情况下，我们都建立了鲁棒的半全局实用渐近或指数稳定性结果，并且我们还展示了如何获得保留原始动力学主要性质的良好定常离散算法。鉴于现有的奇摄动混合系统的平均定理不能直接适用于我们的设置，我们推导了一个扩展的平均定理，它放宽了文献中所做的一些假设，使我们能够在表征混合动力学收敛速率的K - L界与其平均动力学之间建立明确的联系。我们还证明了我们的结果适用于非混合算法，从而为基于平均理论的加速ES动力学提供了一个通用框架。我们给出了不同的数值例子来说明我们的结果。
This paper presents a new class of robust zero-order algorithms for the solution of real-time optimization problems with acceleration. In particular, we propose a family of extremum seeking (ES) dynamics that can be universally modeled as singularly perturbed hybrid dynamical systems with restarting mechanisms. From this family of dynamics, we synthesize four fast algorithms for the solution of convex, strongly convex, constrained, and unconstrained optimization problems. In each case, we establish robust semi-global practical asymptotic or exponential stability results, and we also show how to obtain well-posed discretized algorithms that retain the main properties of the original dynamics. Given that existing averaging theorems for singularly perturbed hybrid systems are not directly applicable to our setting, we derive an extended averaging theorem that relaxes some of the assumptions made in the literature, allowing us to make a clear link between the K L bounds that characterize the rates of convergence of the hybrid dynamics and their average dynamics. We also show that our results are applicable to non-hybrid algorithms, thus providing a general framework for accelerated ES dynamics based on averaging theory. We present different numerical examples to illustrate our results.
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DOI：
10.1109/acc.2015.7171031
发表时间：
2015-07
期刊：
2015 American Control Conference (ACC)
影响因子：
--
作者：
Simon Michalowsky;C. Ebenbauer
通讯作者：
Simon Michalowsky;C. Ebenbauer
影响因子：
--
作者：
V. Grushkovskaya;V. Grushkovskaya;Hans-Bernd Dürr;C. Ebenbauer;A. Zuyev;A. Zuyev
通讯作者：
V. Grushkovskaya;V. Grushkovskaya;Hans-Bernd Dürr;C. Ebenbauer;A. Zuyev;A. Zuyev
影响因子：
3.1
作者：
Fazlyab, Mahyar;Ribeiro, Alejandro;Preciado, Victor M.
通讯作者：
Preciado, Victor M.
影响因子：
3
作者：
Jan Feiling;Amelie Zeller;C. Ebenbauer
通讯作者：
C. Ebenbauer