Hessian-Free Fixed-/Predefined-Time Algorithms for Distributed Time-Varying Optimization

This article proposes distributed algorithms free of Hessian for both time-invariant and time-varying optimization (TVO) problems. To this end, a subsystem is introduced to estimate the system's gradient-sum in a distributed average tracking manner, based on which a distributed protocol is desi...

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Bibliographic Details
Published in:IEEE transactions on systems, man, and cybernetics. Systems Vol. 55; no. 10; pp. 6890 - 6900
Main Authors: Zhou, Zeng-Di, Guo, Ge, Zhang, Renyongkang
Format: Journal Article
Language:English
Published: IEEE 01.10.2025
Subjects:
Accuracy
Approximation algorithms
Convergence
Distributed optimization
fixed-time (FxT)
Germanium
Hessian-free
Linear programming
Multi-agent systems
Optimization
predefined-time (PT)
time-varying optimization (TVO)
Time-varying systems
Upper bound
Vectors
ISSN:2168-2216, 2168-2232
Online Access:Get full text
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Summary:This article proposes distributed algorithms free of Hessian for both time-invariant and time-varying optimization (TVO) problems. To this end, a subsystem is introduced to estimate the system's gradient-sum in a distributed average tracking manner, based on which a distributed protocol is designed by coupling the gradient-sum descent method and state consensus scheme. Additionally, in our TVO method, a norm-normalized signum function is introduced to compensate for the internal drift of the system using its discontinuity. These methods are interesting as they can achieve the optimization goal within a specific time independent of system's initial states, i.e., satisfy fixed-/predefined-time convergence. Moreover, a fully distributed adaptive gain method is proposed to avoid obtaining some global information. The numerical simulation and case study are provided to corroborate the effectiveness of proposed algorithms.
ISSN:2168-2216
2168-2232
DOI:10.1109/TSMC.2025.3593476