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Related Experiment Video

Updated: Feb 6, 2026

Dual-mode Imaging of Cutaneous Tissue Oxygenation and Vascular Function
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Decentralized Primal-Dual Optimization Without Global Lipschitz Continuity.

Luqing Wang, Shaofu Yang, Min-Ling Zhang

    IEEE Transactions on Neural Networks and Learning Systems
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    Summary
    This summary is machine-generated.

    This study introduces adaptive decentralized algorithms (ADPPD and ADPD) for optimization problems, overcoming limitations of existing methods by using local Lipschitz continuity estimates. These scalable algorithms offer faster convergence without needing global Lipschitz constants.

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    Area of Science:

    • Optimization Theory
    • Distributed Systems
    • Machine Learning

    Background:

    • Existing distributed optimization algorithms often require global Lipschitz continuity, which is impractical to estimate and may not hold.
    • The need for accurate Lipschitz constant estimation and global assumptions limits the applicability and performance of current methods.

    Purpose of the Study:

    • To propose novel decentralized algorithms, adaptive decentralized proximal primal-dual (ADPPD) and adaptive decentralized primal-dual (ADPD), for composite optimization problems.
    • To overcome the limitations of existing methods by eliminating the need for global Lipschitz continuity and overly conservative stepsizes.

    Main Methods:

    • Developed two new algorithms, ADPPD and ADPD, featuring adaptive stepsizes within an improved primal-dual framework.
    • Algorithms utilize local estimates of cocoercivity and Lipschitz modulus, avoiding global assumptions.
    • Theoretical analysis to establish convergence rates for convex and strongly convex scenarios.

    Main Results:

    • ADPPD achieves an ergodic convergence rate of $\mathcal {O}(1/k)$ for convex functions.
    • ADPD demonstrates a linear convergence rate when the smooth term is strongly convex.
    • Numerical experiments on least-squares and logistic regression confirm faster convergence compared to existing methods.

    Conclusions:

    • The proposed adaptive decentralized algorithms (ADPPD and ADPD) are effective for composite optimization problems.
    • These algorithms offer improved scalability and faster convergence by leveraging local Lipschitz continuity estimates.
    • The methods eliminate the need for global Lipschitz continuity, enhancing practical applicability.