Fixed-Time Gradient Flows for Solving Constrained Optimization: A Unified Approach

doi:10.1109/JAS.2023.124089

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	Fixed-Time Gradient Flows for Solving Constrained Optimization: A Unified Approach
	Xinli Shi; Xiangping Xu; Guanghui Wen; Jinde Cao
发表期刊	IEEE/CAA Journal of Automatica Sinica
ISSN	2329-9266
	2024
卷号	11 期号:8 页码:1849-1864
摘要	The accelerated method in solving optimization problems has always been an absorbing topic. Based on the fixed-time (FxT) stability of nonlinear dynamical systems, we provide a unified approach for designing FxT gradient flows (FxTGFs). First, a general class of nonlinear functions in designing FxTGFs is provided. A unified method for designing first-order FxTGFs is shown under Polyak-Łjasiewicz inequality assumption, a weaker condition than strong convexity. When there exist both bounded and vanishing disturbances in the gradient flow, a specific class of nonsmooth robust FxTGFs with disturbance rejection is presented. Under the strict convexity assumption, Newton-based FxTGFs is given and further extended to solve time-varying optimization. Besides, the proposed FxTGFs are further used for solving equation-constrained optimization. Moreover, an FxT proximal gradient flow with a wide range of parameters is provided for solving nonsmooth composite optimization. To show the effectiveness of various FxTGFs, the static regret analyses for several typical FxTGFs are also provided in detail. Finally, the proposed FxTGFs are applied to solve two network problems, i.e., the network consensus problem and solving a system linear equations, respectively, from the perspective of optimization. Particularly, by choosing component-wisely sign-preserving functions, these problems can be solved in a distributed way, which extends the existing results. The accelerated convergence and robustness of the proposed FxTGFs are validated in several numerical examples stemming from practical applications.
关键词	Consensus constrained optimization disturbance rejection linear equations fixed-time gradient flow (FxTGF)
DOI	10.1109/JAS.2023.124089
引用统计
文献类型	期刊论文
条目标识符	http://ir.ia.ac.cn/handle/173211/58552
专题	学术期刊_IEEE/CAA Journal of Automatica Sinica
推荐引用方式 GB/T 7714	Xinli Shi,Xiangping Xu,Guanghui Wen,et al. Fixed-Time Gradient Flows for Solving Constrained Optimization: A Unified Approach[J]. IEEE/CAA Journal of Automatica Sinica,2024,11(8):1849-1864.
APA	Xinli Shi,Xiangping Xu,Guanghui Wen,&Jinde Cao.(2024).Fixed-Time Gradient Flows for Solving Constrained Optimization: A Unified Approach.IEEE/CAA Journal of Automatica Sinica,11(8),1849-1864.
MLA	Xinli Shi,et al."Fixed-Time Gradient Flows for Solving Constrained Optimization: A Unified Approach".IEEE/CAA Journal of Automatica Sinica 11.8(2024):1849-1864.

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